(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.
(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.
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 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 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.
(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 attains
a maximum value at some x.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd309db8b-57e0-4182-b683-2059130ecfe2%2Fff107246-6a96-46ee-93dc-28554c696530%2F7z3tuoq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(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.
(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 attains
a maximum value at some x.
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