8 Graph the function y = x4 - 10x2 = x2(x2 -10) 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 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. O A. The function is an odd function that is symmetric about the y-axis. O B. The function is an even 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 origin. O E. The function is neither even nor odd. Find the derivative y'. у 3 Find the second derivative y". 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= (Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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 increases on the open interval(s) and does not decrease (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O B. The curve does not increase and decreases on the open interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O C. The curve increases on the open interval(s) and decreases on the open interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O B. The curve is concave up on the interval(s) and is concave down on the interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O C. The curve is never concave up and is concave down on the interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. 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 (Type equations.) O C. The function has no vertical asymptotes. and the rightmost asymptote is 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 and the asymptote with larger slope is (Type equations.) O C. The function has no oblique asymptotes. Graph the function y x4 - 10x2. Choose the correct graph O A. O B. -10 10 50- O C. O D. 10- -10 10 50 -50- 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 = (Round to the nearest tenth as needed. 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 = (Round to the nearest tenth as needed. Use a comma to separate answers as needed. Type each answer only once.) O B. There is no absolute minimum.
8 Graph the function y = x4 - 10x2 = x2(x2 -10) 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 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. O A. The function is an odd function that is symmetric about the y-axis. O B. The function is an even 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 origin. O E. The function is neither even nor odd. Find the derivative y'. у 3 Find the second derivative y". 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= (Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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 increases on the open interval(s) and does not decrease (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O B. The curve does not increase and decreases on the open interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O C. The curve increases on the open interval(s) and decreases on the open interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O B. The curve is concave up on the interval(s) and is concave down on the interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.) O C. The curve is never concave up and is concave down on the interval(s) (Type your answer in interval notation. Round to the nearest tenth as needed. 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 (Type equations.) O C. The function has no vertical asymptotes. and the rightmost asymptote is 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 and the asymptote with larger slope is (Type equations.) O C. The function has no oblique asymptotes. Graph the function y x4 - 10x2. Choose the correct graph O A. O B. -10 10 50- O C. O D. 10- -10 10 50 -50- 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 = (Round to the nearest tenth as needed. 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 = (Round to the nearest tenth as needed. Use a comma to separate answers as needed. Type each answer only once.) O B. There is no absolute minimum.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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Transcribed Image Text:8
Graph the function y = x4 - 10x2 = x2(x2 -10) 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 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.
O A. The function is an odd function that is symmetric about the y-axis.
O B. The function is an even 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 origin.
O E. The function is neither even nor odd.
Find the derivative y'.
у 3
Find the second derivative y".
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=
(Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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 increases on the open interval(s)
and does not decrease
(Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
O B. The curve does not increase and decreases on the open interval(s)
(Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
O C. The curve increases on the open interval(s)
and decreases on the open interval(s)
(Type your answer in interval notation. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. 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. Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
O B. The curve is concave up on the interval(s)
and is concave down on the interval(s)
(Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
O C. The curve is never concave up and is concave down on the interval(s)
(Type your answer in interval notation. Round to the nearest tenth as needed. Use a comma to separate answers as needed.)
O D. The curve is neither concave up nor concave down.
Transcribed Image Text: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
(Type equations.)
O C. The function has no vertical asymptotes.
and the rightmost asymptote is
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
and the asymptote with larger slope is
(Type equations.)
O C. The function has no oblique asymptotes.
Graph the function y x4 - 10x2. Choose the correct graph
O A.
O B.
-10
10
50-
O C.
O D.
10-
-10
10
50
-50-
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 =
(Round to the nearest tenth as needed. 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 =
(Round to the nearest tenth as needed. Use a comma to separate answers as needed. Type each answer only once.)
O B. There is no absolute minimum.
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