Let the functionf be continuous on the closed interval [a, b] and differentiable with derivative f' on the open interval (a, b). Suppose futher that f(a) = f(b) = k. Then there is a point c in (a, b) such that f'(c) = 0. True O False

Let the functionf be continuous on the closed interval [a, b] and differentiable with derivative f' on the open interval (a, b). Suppose futher that f(a) = f(b) = k. Then there is a point c in (a, b) such that f'(c) = 0. True O False

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

See similar textbooks

Related questions

Q: Use the definition to calculate the derivative of the criterion of the function f(x) = e14x. In…

Q: Use the limit definition of the derivative to prove the following special case of the Product Rule:

A: The derivative of the function is the rate of change of the value of the function when the value of…

Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 7.

Q: Compute the derivative of f (x) = x3/2 using the limit definition. Hint: Show that

A: we have; f(x)=x32

Q: If f is continuous at a number, x, then f is differentiable at x. True False

Q: 2. f(x) = Vx – 1 at x = 5

A: Function is continuous and differentiable both at x= 5.....for detail...go through the solution

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

Q: Find the equation of the tangent line of f(x) = sqrt(x+1) at x = 0 using the definition of limits.

A: To find: The equation of tangent of line. Given: The function is f(x)=x+1. Concept used: Slope…

Q: If the derivative of y=f(x) does not exist at X = a then y f(x) is not continuous at X = A) True B)…

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

Q: Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be…

Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: Give an example of a function that is continuous on -∞ < x < o but is not differentiable at x = 3.

Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: Find the derivative of f(x) at r = 0 using the definition of the derivative as a limit. %3D Va +I

Q: Let f(x) = √x. Find the derivative of f(x) at x = 2 by using the definition of the derivative as a…

Q: Express the limit as a derivative.

A: Our Aim is to evaluate the limit of the expression given below:-limt→πsin (t) cos (t)t-π-(i)

Q: Show that the function is continuous on (∞ , -∞).

Q: Suppose that fx) is continuous on [0, 9] and F(x) is an anti-derivative of f. If F(0)=9 and F(9)=7,…

A: Given that: f(x) is continuous in [0, 9].…

Q: Use limits to determine if f(x) = 1 is continuous at x = 0. (z+2)?

Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: To prove that given function is continuous. gx,y=xy3x2+y6, if x,y≠0,00, if x,y=0,0

Q: Suppose f is differentiable with continuous derivative on [a, b]. Show that lim f(x) sin(nx) dr = 0.

A: To prove the given limit

Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Prove that if the function f : I → R has a bounded derivative on I, then f is uniformly continuous…

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 11.

A: Here we have to use limit definition to find derivative

Q: Show that the function f(z) = sin x cosh y + i cos x sinh y is continuous as well as analytic every…

Q: are differentiable at a, then prove the sum and product rules for derivatives. If f, 9

Q: Are there independent linear functions with derivative number n – 1 continuous 91 ,..., „,with…

Q: if x = 0 f (x) = %3D x* sin(-) otherwise

A: In the given question, concept of continuity is applicable. Continuity Continuity for a graph y=fx…

Q: Let Q = Q(K, L, t), where K is capital, L is labor, and t is time. Both capital and labor as also…

A: Let the production function is Q = Q (K , L , t)…

Q: Let y be a function of x and suppose y= In(y-x). What is the correct result for the derivative of y…

Q: Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.…

A: We have to find

Q: Suppose that the functions f and g are defined throughout an open interval containing the point x,,…

Q: Let ƒ be a function that is continuous on [0, 2] and đifferentiable on (0, 2). Suppose that f (0) <…

A: Yes, we will show that f' necessarily take on both positive and negative values on (0, 2). If the…

Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

Q: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

Q: 1. Let f(x) = 2 %3D Use the limit definition of the derivative to compute f'(-1). X+3

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

Q: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

Q: (a) (b) Explain the differentiability of f on R by using definition. Let f' be the first derivative…

Q: Explain the difference between a function f(x) being continuous at the point x=a and the limit…

A: We need to find the difference between function is continuous at x=a and limit exists at x=a

Q: 1 . Let f(r) 2r + 1

Q: Show that the function f(z)=sin x coshy+I cosx sinh y is continuous as well as analytic every where

Question

100%

Let the function f be continuous on the closed interval [a, b and differentiable with derivative f' on the open interval (a, b).
Suppose futher that f(a) = f(b) =
k. Then there is a point c in (a, b) such that f'(c) = 0.
True
False

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 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Complexity$

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

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.
What is the purpose of the Intermediate Value Theorem?
Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0, 1). Prove that f' is continuous on (0, 1).
Let f(x) be a function that is defined and has a continuous derivative on the interval (2,∞). Assume also that f(3)=−12. |f(x)|<x^4+8 and ∫ [3,∞] f(x)e-x/3dx=−9 Determine the value of ∫ [3,∞] f ' (x)e-x/3dx
Consider a function f continuous and differentiable on R with f(2. 5) = -3. 1 and f'(2. 5)=-0. 2.Use a tangent line to approximate the function value f(2. 2)
Let f:Rto R be a continuous function that is convex on ( -infinity,0] and [0,infinity) and has a local maximum at the point 0 . Prove that the function is not differentiable at the point 0 .
Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be the boundary of the region in the xy-plane that is bounded below by the x-axis, above by the graph of ƒ, and on the sides by the lines x = a and x = b. Show that ∫ƒ(x) dx = - ∮C y dx.
Let f : I → J be a bijective differentiable function froman interval I to an interval J, and let F : I → R be an anti-derivative of f. Find an explicit expression, in terms of f, f-1 and F, for an anti-derivative of f-1: J → I. [Both substitution and integration by parts may come in handy.]
Examine if f(x) = ln(x2+2) is uniform continuous on the interval (-∞,∞)