Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e-2x, [o, 1] O Yes, f is continuous and differentiable on R, so it is continuous on [0, 1] and differentiable on (0, 1). O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O No, fis continuous on [0, 1] but not differentiable on (0, 1). O No, fis not continuous on [0, 1). O There is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).

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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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = e-2x, [O, 1]
O Yes, f is continuous and differentiable on R, so it is continuous on [0, 1] and differentiable on (0, 1).
O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.
O No, f is continuous on [0, 1] but not differentiable on (0, 1).
O No, f is not continuous on [0, 1].
O There is not enough information to verify if this function satisfies the Mean Value Theorem.
If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter
DNE).
Transcribed Image Text:Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e-2x, [O, 1] O Yes, f is continuous and differentiable on R, so it is continuous on [0, 1] and differentiable on (0, 1). O Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem. O No, f is continuous on [0, 1] but not differentiable on (0, 1). O No, f is not continuous on [0, 1]. O There is not enough information to verify if this function satisfies the Mean Value Theorem. If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list. If it does not satisfy the hypotheses, enter DNE).
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