Question

Can I get help with this problem step by step?

14.
Graph the function y =
Зx
by identifying the domain and any symmetries, finding the derivatives y' and y", finding the critical points and identifying the function's behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and
x2 - 25
plotting any key points such as intercepts, critical points, and inflection points. Then find coordinates of absolute extreme points, if any
Find the domain of the function
The domain is
(Type your answer in interval notation.)
Identify any symmetries. Choose the correct answer below.
OA. The function is an even function that is symmetric about the origin
O B. The function is an odd function that is symmetric about the origin
O C. The function is an even function that is symmetric about the y-axis.
O D. The function is an odd function that is symmetric about the y-axis.
O E. The function is neither even nor odd
Find the derivative y'.
у'%3
Find the second derivative y'"
у'3
Identify any critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The critical point(s) occur(s) at x =
(Use a comma to separate answers as needed.)
O B. There are no critical points.
Identify any local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The local minimum/minima is/are located at
(Type an ordered pair. Use a comma to separate answers as needed.)
O B. There are no local minima.
Identify any local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice
O A. The local maximum/maxima is/are located at
(Type an ordered pair. Use a comma to separate answers as needed.)
O B. There are no local maxima
Identify where the curve is increasing or decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The curve does not increase and decreases on the open interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O B. The curve increases on the open interval(s)
and decreases on the open interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O C. The curve increasess on the open interval(s)
and does not decrease
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O D. The curve neither increases nor decreases.
Identify any inflection points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The inflection point(s) is/are at
(Type an ordered pair. Use a comma to separate answers as needed.)
O B. There are no inflection points.
expand button
Transcribed Image Text:14. Graph the function y = Зx by identifying the domain and any symmetries, finding the derivatives y' and y", finding the critical points and identifying the function's behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and x2 - 25 plotting any key points such as intercepts, critical points, and inflection points. Then find coordinates of absolute extreme points, if any Find the domain of the function The domain is (Type your answer in interval notation.) Identify any symmetries. Choose the correct answer below. OA. The function is an even function that is symmetric about the origin O B. The function is an odd function that is symmetric about the origin O C. The function is an even function that is symmetric about the y-axis. O D. The function is an odd function that is symmetric about the y-axis. O E. The function is neither even nor odd Find the derivative y'. у'%3 Find the second derivative y'" у'3 Identify any critical points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) occur(s) at x = (Use a comma to separate answers as needed.) O B. There are no critical points. Identify any local minima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The local minimum/minima is/are located at (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no local minima. Identify any local maxima. Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The local maximum/maxima is/are located at (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no local maxima Identify where the curve is increasing or decreasing. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The curve does not increase and decreases on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The curve increases on the open interval(s) and decreases on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O C. The curve increasess on the open interval(s) and does not decrease (Type your answer in interval notation. Use a comma to separate answers as needed.) O D. The curve neither increases nor decreases. Identify any inflection points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The inflection point(s) is/are at (Type an ordered pair. Use a comma to separate answers as needed.) O B. There are no inflection points.
Identify where the curve is concave up or concave down. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The curve is concave up on the interval(s)
and is never concave down.
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O B. The curve is never concave up and is concave down on the interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O C. The curve is concave up on the interval(s)
and is concave down on the interval(s)
(Type your answer in interval notation. Use a comma to separate answers as needed.)
O D. The curve is neither concave up nor concave down.
Find any vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The function has one vertical asymptote,
(Type an equation.)
O B. The function has two vertical asymptotes. The leftmost asymptote is
and the rightmost asymptote is
(Type equations.)
O C. The function has no vertical asymptotes.
Find any horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The function has one horizontal asymptote,
(Type an equation.)
O B. The function has two horizontal asymptotes. The top asymptote is
and the bottom asymptote is
(Type equations.)
O C. The function has no horizontal asymptotes.
Find any oblique asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The function has one oblique asymptote,
(Type an equation.)
O B. The function has two oblique asymptotes. The asymptote with smaller slope is
(Type equations.)
and the asymptote with larger slope is
O C. The function has no oblique asymptotes.
Зx
Choose the correct graph
Graph the function y
x2 -25
O A.
ОВ.
Ay
Ay
гА
10
10
10
10
10-
O D.
Ос.
10
10
10
10
Identify the absolute maximum value and where it occurs. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice
O A. The absolute maximum value
occurs at x = |
(Use a comma to separate answers as needed. Type each answer only once.)
O B. There is no absolute maximum
Identify the absolute minimum value and where it occurs. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
O A. The absolute minimum value
OCcurs at x =
(Use a comma to separate answers as needed. Type each answer only once.)
O B. There is no absolute minimum.
expand button
Transcribed Image Text:Identify where the curve is concave up or concave down. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The curve is concave up on the interval(s) and is never concave down. (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The curve is never concave up and is concave down on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O C. The curve is concave up on the interval(s) and is concave down on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O D. The curve is neither concave up nor concave down. Find any vertical asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has one vertical asymptote, (Type an equation.) O B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is (Type equations.) O C. The function has no vertical asymptotes. Find any horizontal asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has one horizontal asymptote, (Type an equation.) O B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is (Type equations.) O C. The function has no horizontal asymptotes. Find any oblique asymptotes. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has one oblique asymptote, (Type an equation.) O B. The function has two oblique asymptotes. The asymptote with smaller slope is (Type equations.) and the asymptote with larger slope is O C. The function has no oblique asymptotes. Зx Choose the correct graph Graph the function y x2 -25 O A. ОВ. Ay Ay гА 10 10 10 10 10- O D. Ос. 10 10 10 10 Identify the absolute maximum value and where it occurs. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice O A. The absolute maximum value occurs at x = | (Use a comma to separate answers as needed. Type each answer only once.) O B. There is no absolute maximum Identify the absolute minimum value and where it occurs. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The absolute minimum value OCcurs at x = (Use a comma to separate answers as needed. Type each answer only once.) O B. There is no absolute minimum.
Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Not helpful? See similar books
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Functions And Models. 1RCC
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: 4. Sketch the graph of a function y = f(r) satisfying the following information: • Domain: (-0, -1)…

A: Click to see the answer

Q: 12. Determine the following and use algorithm to sketch the curve given by the function f(x) = x³ +…

A: The given function is f(x)=x3+6x2+9x Note:   Multiple sub parts are given, we are answered with only…

Q: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: 1. Consider the following function: f (x) 2x2 – x4 A. Find the critical values. B. Use the "Second…

A: Click to see the answer

Q: The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells…

A: Click to see the answer

Q: 4.20 Consider the function f(x) = x' – 2x + 4 on the interval [-2, 2] with h = 0.25. Use the…

A: Click to see the answer

Q: 16) what are the vertical asymptote(s) of f(x) = x+5x-6, %3D x² -1

A: Click to see the answer

Q: Find the critical numbers of the function f(x) = 14x + |x|. In the answer boxes below, enter the…

A: Given: f(x)=14x3+|x| Definition: Critical points are the points where the derivative of function is…

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: 7) a) Find all the critical points of the function y = h(x) = ln(x +1)° – 2x + 5. b) For each…

A: Given      y = ln(x+1)^6-2x+5

Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

A: Click to see the answer

Q: 1. Use the Cauchy-Riemann equation to determine if the function f(z) = x3 - i(2 - y)3 is analytic or…

A: Use Cauchy-Riemann equation to determine if the function f(z)

Q: 5) Find all possible oblique asymptotes for following functions: y = Vx² + 1 2x/2+2x-3 y = Vx+1 y =…

A: Click to see the answer

Q: Sketch the graph of y = (x² – 2)² – x². [In your answer, you must include the following: • Find the…

A: We have to sketch the graph of function y=x2-22-x2

Q: For the function f (x) = x + 2sin (x), x > 0 , use calculus methods to find the following (if any):…

A: E)

Q: Consider the following function. f(x) = x2 - 4x (a) Find the critical numbers of f. (Enter your…

A: Click to see the answer

Q: Use the given derivative to find all critical points of /, and at each critical point determine…

A: Click to see the answer

Q: Let 1² +1 f(x) = (i) Vertical and horizontal asymptotes are r = ... and y =.. (ii) f'(x) = -$ (iii)…

A: Click to see the answer

Q: Determine {f],where the periodic function is described by its graph. 19 2a 3a 40 (1-as) (1-) 1.…

A: Click to see the answer

Q: 3. Find the Absolute Minimum and Absolute Maximum of f(x,y)=xy subject to 2x² +8y² =144 Fully…

A: Click to see the answer

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

A: The derivative of the function f is f'(x)=2-3xx+83

Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

A: Click to see the answer

Q: Let f(x) =  8 x2 − 4x. Then its first derivative is f'(x) =  32 − 16x (x2 − 4x)2. a. Find the…

A: Given that fx=8x2-4xf'x=32-16xx2-4x2

Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: 10. Discuss the characteristics of the periodic function f(0)= 6 in the range -n<0<a (period 21)…

A: Plot graph of periodic form of f(θ).

Q: 26 a. The function f(x)=x- 6x² + 9x-3 is defined on the interval [0,5]. Find the critical points of…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: Consider the following function. f(x) = 5x +- (a) Find the critical numbers of f. (Enter your…

A: Function given is - f(x)=5x+1x Differentiate with respect to x- f'(x)=5-1x2  [since ddx1x=-1x2]a) To…

Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given, f'x=21-x21+x2                         ...(1) and f''x=4xx2-31+x22

Q: 4) For any funchion f(x), the solutions to the eguation f'(^) = 0 critical point. give the values of…

A: Solve the following

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

A: Click to see the answer

Q: Consider the following function. f(x) = 2 - |x - | (a) Find the critical numbers off. (Enter your…

A: To find the critical number

Q: 10. Discuss the characteristics of the periodic function f(0)=0² in the range -n<0<n (period 2 )…

A: Click to see the answer

Q: 10. Discuss the characteristics of the periodic function f(0)= 0² in the range -n<0<n (period 2r )…

A: Click to see the answer

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

A: Click to see the answer

Q: 6. Sketch an even continuous function with all of the following features: • Absolute maximum at 6 •…

A: We can solve this using given information As we know the even function is nothing but symmetric…

Q: Suppose k is the derivative of K, a function with the same domain as k. The function K has one…

A: The function K has one critical point at t =0.Use a number line and the first derivative test to…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A: Click to see the answer

Q: 2. Find the global maximum and global minimum of f(x) = xe- on [0, 6].

A: Click to see the answer

Q: 7. What does the critical point(s) mean to the graph of the function? Determine the critical…

A: Critical points of graph of function points on graph of function where derivative is zero or…

Q: The purpose of this question is to do the preliminary work to make a well-labeled sketch of the…

A: Click to see the answer

Q: ose k is the derivative of K, a function with the same domain as k. inction K has one critical point…

A: According to answer policy we can answer one question at a time, therefore I will be answering first…

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781285741550
    Author:James Stewart
    Publisher:Cengage Learning
    Thomas' Calculus (14th Edition)
    Calculus
    ISBN:9780134438986
    Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
    Publisher:PEARSON
    Calculus: Early Transcendentals (3rd Edition)
    Calculus
    ISBN:9780134763644
    Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
    Publisher:PEARSON
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781319050740
    Author:Jon Rogawski, Colin Adams, Robert Franzosa
    Publisher:W. H. Freeman
    Precalculus
    Calculus
    ISBN:9780135189405
    Author:Michael Sullivan
    Publisher:PEARSON
    Calculus: Early Transcendental Functions
    Calculus
    ISBN:9781337552516
    Author:Ron Larson, Bruce H. Edwards
    Publisher:Cengage Learning
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781285741550
    Author:James Stewart
    Publisher:Cengage Learning
    Thomas' Calculus (14th Edition)
    Calculus
    ISBN:9780134438986
    Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
    Publisher:PEARSON
    Calculus: Early Transcendentals (3rd Edition)
    Calculus
    ISBN:9780134763644
    Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
    Publisher:PEARSON
    Calculus: Early Transcendentals
    Calculus
    ISBN:9781319050740
    Author:Jon Rogawski, Colin Adams, Robert Franzosa
    Publisher:W. H. Freeman
    Precalculus
    Calculus
    ISBN:9780135189405
    Author:Michael Sullivan
    Publisher:PEARSON
    Calculus: Early Transcendental Functions
    Calculus
    ISBN:9781337552516
    Author:Ron Larson, Bruce H. Edwards
    Publisher:Cengage Learning