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Explain why each of the following statements is false. Make sure you justify clearly, using words, cific counterexamples, and/or graphs. 1. If f(x) is defined on (a, b) and f(c) = 0 at some point c E (a, b), then f'(c) = 0.

Explain why each of the following statements is false. Make sure you justify clearly, using words, cific counterexamples, and/or graphs. 1. If f(x) is defined on (a, b) and f(c) = 0 at some point c E (a, b), then f'(c) = 0.

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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Explain why each of the following statements is false. Make sure you justify clearly, using words, ecific counterexamples, and/or graphs. 1. If x) is defined on (a, b) and f(c) = 0 at some point c E (a, b), then f'(c) = 0. 2x + 1 if x < 0 2. If f(x) : then f'(0) = 2. x + 2x if x > 0 3. The tangent line to f at the point where x = a intersects f at exactly one point. 4. If f'(x) > g' (x) for all x E (a, b), then f(x) > g(x) for all x E (a, b). 5. If ƒ is a function and f2 is differentiable everywhere, then f is differentiable everywhere.
Transcribed Image Text:Explain why each of the following statements is false. Make sure you justify clearly, using words, ecific counterexamples, and/or graphs. 1. If x) is defined on (a, b) and f(c) = 0 at some point c E (a, b), then f'(c) = 0. 2x + 1 if x < 0 2. If f(x) : then f'(0) = 2. x + 2x if x > 0 3. The tangent line to f at the point where x = a intersects f at exactly one point. 4. If f'(x) > g' (x) for all x E (a, b), then f(x) > g(x) for all x E (a, b). 5. If ƒ is a function and f2 is differentiable everywhere, then f is differentiable everywhere.
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