Answered: find value of A if f(x) is continuous…

Math

Calculus

find value of A if f(x) is continuous at x=2 if f(x)={x−1,x<2 {ax+3,x≥2

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.6: Analyzing Graphs Of Functions

Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

See similar textbooks

Related questions

Q: Find the critical points of f(x) = x® (x – 4) = x8 – 4x!a Identify the intervals on which f is…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Determine f(x) = x2 + x-2 is continuous on the given interval (-0,+0) (show graph and its table…

A: Here, the given function is: f(x)=x2+x-2 And the given interval is (-∞,∞).

Q: f(x) = x^2/3 show that there is no number c in interval (-1,8) that satisfies f’(c)=…

Q: Every differentiable function y= f(x) defined on an open interval (a, b) has an absolute maximum and…

A: True

Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,9] by comparing…

A: Given, fx=lnxx on the interval 1,9

Q: Find the absolute maxima and minima for f(x) on the interval [a, b]. f(x) = x3 − 6x2 − 36x + 6,…

A: For absolute maximum and minimum we need to check value of f(x) on boundary values of intervals and…

Q: 3. Determine f(x) = x +x-2 is continuous on the given interval (-0,+0) (show graph and its table of…

Q: Generate a continuous and differentiable function f(x) with the following properties: f(x) is…

A: Given that f(x) is decreasing at x=−6 f(x) has a local minimum at x=−3 f(x) has a local maximum at…

Q: The value (x, f(x)) of the maximum or minimum limit of the function 8 + f(x) = x3 - 6x2 + 4x and for…

A: Please see the attachment

Q: 4 – x2, - 2x, X 0

A: given f(x)=4-x2, x≤0-2x, x>0

Q: The function f (x) = 2x³ + 9x? and has critical numbers x = -4 and x = 1. To determine where f…

A: Option A is correct. We find Maxima and minima on critical points and given interval values.

Q: Find the Absolute Extrema of f(x), on the given closed interval. f(x) = 3x² – 2x³; [-5,1] (A No…

A: The given function f(x)=3x2-2x3 Take the derivative of the original function…

Q: ppose we know that f(x) is continuous and differentiable on [2, 14], with f(2)= -5 and f'(x) <= 10.…

A: Given data: The given interval is [a,b]=[2,14]. The given value of f(2) is f(2)=-5. The given…

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

Q: ) Suppose f (x) is continuous on [0, 2] and differentiable on (0,2). Suppose f (0) = 3 and f (2) =…

A: Use the concept of Roll's Theorem and Extreme Value theorem and solve the problems.

Q: 2 For the f(x)=2x² - 4x² defined -2≤x≤3 on the interval A. Find all critical points B. Find absolute…

Q: 3. f(x) = Vx - 5 is continuous on the interval [5, 0) %3D

Q: Find numbers a and b, so that f is continuous at every point. f(x)= 20 , x-1

Q: FIND a) F(5) b)interval over which F(x) is decreasing c) what x=? Where F(x) has a maximum value

A: Given, F(x)=∫0xf(t)dt Graph,

Q: A continuous function f satisfies the equation 1 f (x) = x – t+ 2 f(t) dt 0, For all x e [-1, 3].…

A: We have to use leibiniz rule of differentiating definite integral d∫f(x)g(x)h(t)…

Q: A function, f (x), has derivatives: f'(x) = x² (x – 3) f"(x) = 3x(x – 2) Which of the following…

A: Given data is : A function, fx, has derivativef'x=x2x-3f''x=3xx-2

Q: Show (in terms of epsilon - delta ) that a function f : [2 ; 7] follows R be defined by f(x)…

Q: 3) Determine the value(s) of k that make the functionf (x) continuous for all x. Show your work for…

Q: Find the critical number of the function F(x)= x^-8In(x) X=

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 +8x + 15…

Q: Consider the function f(x) = 7x + 5x-¹. For this function there are four important intervals: ( ∞,…

Q: Consider the function f(x) = 4x + 2x^-1 For this function there are four important intervals. (-∞,…

Q: Let f(x) = -9+ 8x – a³. (A) Find the critical values of f(x). Critical values: (B) Use interval…

Q: True or False. If f(x) is a differentiable function such that f '(-1) = 0, then f(x) either has a…

A: we have to tell that statement is true or false. If f(x) is a differentiable function such that f…

Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,6] by comparing…

A: The given function is: f(x)=ln xx

Q: The second derivative f" is defined on the closed interval [0, 8n]. Now test f" in the intervals (0,…

A: use the definition of concave upward and concave downward .

Q: For the function f(x)= x73 – 4 (a) find the critical numbers (b) find the open intervals on which…

A: Given function is f'(x)=0 for no value of x. Also f'(x) is not defined for x=0. Therefore, only…

Q: Determine the value of the constant a for which the function f(x) is continuous at - 3. x2 + 8x + 15…

Q: Find the critical numbers of the function. f(x) = x5 - 5x4 Step 1 To find the critical numbers of f,…

Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,9] by comparing…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find all the intervals at which the given function is continuous. 1. f(x) = x - 3x - 10 2. g(x) =…

A: Disclaimer: Since you have posted multiple questions, we will answering the first the questions for…

Q: Consider the function f(x) = 9x + 4x-1. For this function there are four important intervals: (- 00,…

Q: For the function g(x) = 3x2e-x (a) Find all critical numbers. (b) Find the intervals on which g(x)…

A: Given that, gx=3x2e-x ...(1)

Q: Consider the function f(x) = 2a + 24z 42x + 1. - Find the critical numbers. 7,1 On what interval(s)…

A: Explanation of the answer is as follows

Q: The critical points of the function f(x) 16x2 2x4 occur at - O x = = 0, x = ±1.60 x = 0, x = ±2.67 O…

Q: A continuous function, h(x) has a local maximum at (2, 3). What is h’(2)?

A: We have given that h(x) is a continuous function and has a local maximum at point (2,3).

Q: Consider the function g(x) = x2 (x – 2)² ° (a) Find the critical points of g(x). (b) Find the…

A: gx=x2x-22 Differentiating with respect to x, we get g'x=dx2dx·x-22-dx-22dx·x2x-222…

Q: The function fis continuous on the closed interval [-1, 1] and has values that are given in the…

Q: f f (x) has a local maximum, but no absolute maximum, in the interval [-5,5], then f (x) cannot be…

Q: 3. Discuss the continuity of the ff. functions. (Consider all the possible points of discontinuity.…

A: Solution is given below:

Q: (x + 1, x 0 Can also be displayed as: x + 1 when x 0 f(x) = Is f(x) continuous at x = 0? Why or why…

A: We have to find the solution of continuity

Q: (a). Find the values of a and b that make f continuous everywhere. x² -4 if x<2 x-2 f(x)={ax² - bx+3…

A: f(x)=x2-4x-2if x<2ax2-bx+3if 2≤x<32x- a+bif x≥3 Definition: Continuous functionLet f(x) be a…

Q: Provide an appropriate response. The critical values of f(x) = 4x - 48x + 24 are x = -2 and x = 2.…

A: The critical values of the function fx=4x3-48x+24 are x=-2 and x=2. To find : Which of the critical…

Q: Find the critical numbers of the function. f(x) = x5 - 5x Step 1 o or f (x) does not exist. does not…

A: We need to find the critical numbers of the functionfx=x5-5x4

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

find value of A if f(x) is continuous at x=2 if
f(x)={x−1,x<2
{ax+3,x≥2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Limits and Continuity$

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.

Similar questions

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?
Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.