Explain why false/true (a) True or False: If f'(x) = g'(x) then f(x) = g(x).(b) True or False: If f'(-1) equals 0 then f has either a local minimum or alocal maximum at x = -1.(c) True or False: If f is differentiable at x = -1 and has a local minimum atx = -1, then f'(-1) = 0.(d) True or False: All integrable functions must be differentiable.(e) True or False: If f is a continuous function with domain [0, 1] then f attainsa maximum value at some x.

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Answered: (a) True or False: If f'(x) = g'(x)…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

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(a) True or False: If f'(x) = g'(x) then f(x) = g(x). (b) True or False: If f'(-1) equals 0 then f has either a local minimum or a local maximum at x = -1. (c) True or False: If f is differentiable at x = -1 and has a local minimum at x = -1, then f'(-1) = 0.