In the function f(x), find the value of c that satisfies the Mean Value Theorem f(x) = -x³+4x² - 3, [0, 4] 3

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In the function f(x), find the value of c that satisfies the Mean Value Theorem
ƒ(x) = −x³ + 4x² – 3, [0, 4]
3
Your answer
Transcribed Image Text:In the function f(x), find the value of c that satisfies the Mean Value Theorem ƒ(x) = −x³ + 4x² – 3, [0, 4] 3 Your answer
Rolle's Theorem and Mean Value Theorem
Consider the function f(x) on the interval [-1, 1]. Which of the three hypotheses of
Rolle's Theorem fails for this function on the interval?
f(x) = 9-9x²/3
Of(x) is continuous on [-1, 1]
Of(x) is differentiable on (-1, 1)
Of(-1)=f(1)
Suppose that f(0) =-1 and f'(x)<=2 for all values of x. Use the Mean Value Theorem
to determine how large f(4) can possibly be. f(4) <=?
Your answer
Transcribed Image Text:Rolle's Theorem and Mean Value Theorem Consider the function f(x) on the interval [-1, 1]. Which of the three hypotheses of Rolle's Theorem fails for this function on the interval? f(x) = 9-9x²/3 Of(x) is continuous on [-1, 1] Of(x) is differentiable on (-1, 1) Of(-1)=f(1) Suppose that f(0) =-1 and f'(x)<=2 for all values of x. Use the Mean Value Theorem to determine how large f(4) can possibly be. f(4) <=? Your answer
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