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Consider the following function. f(x) = 16 – x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all values c in (-64, 64) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C =

Consider the following function. f(x) = 16 – x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all values c in (-64, 64) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C =

Calculus: Early Transcendentals
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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Consider the following function. f(x) = 16 – x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all values c in (-64, 64) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f is differentiable, f(-64) = f(64), and f'(c) = 0 exists, but c is not in (-64, 64). O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-64, 64). O This contradicts Rolle's Theorem, since f(-64) = f(64), there should exist a number c in (-64, 64) such that f'(c) = 0. O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-64, 64). O Nothing can be concluded.
Transcribed Image Text:Consider the following function. f(x) = 16 – x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all values c in (-64, 64) such that f'(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) C = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f is differentiable, f(-64) = f(64), and f'(c) = 0 exists, but c is not in (-64, 64). O This does not contradict Rolle's Theorem, since f'(0) = 0, and 0 is in the interval (-64, 64). O This contradicts Rolle's Theorem, since f(-64) = f(64), there should exist a number c in (-64, 64) such that f'(c) = 0. O This does not contradict Rolle's Theorem, since f'(0) does not exist, and so f is not differentiable on (-64, 64). O Nothing can be concluded.
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