(a) Any critical point of a function f is either a local maximum or local minimum for f.TrueFalse(b) Every differentiable function is continuous.TrueFalse(c) Any function ƒ defined on a closed interval [a, b] is guaranteed to have a global maximum, and this maximum mustoccur either at a critical point of f in the open interval (a, b) or at one of the endpoints a or b.TrueFalse(d) Any local minimum or local maximum of a function f must occur at a critical point of f. TrueFalse(e) Every function f defined on (-∞, 0) that satisfies the condition that lim f(x) =lim f(x) = o must have at leastX -0one critical point.TrueFalse(f) The function f(x) = Vx is differentiable at x =0.TrueFalse(g) The function f(x) = |x| is not continuous at x = 0.O TrueFalse

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Answered: (a) Any critical point of a function f…

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(a) Any critical point of a function f is either a local maximum or local minimum for f. True False

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

(a) Any critical point of a function f is either a local maximum or local minimum for f.
True
False
(b) Every differentiable function is continuous.
True
False
(c) Any function ƒ defined on a closed interval [a, b] is guaranteed to have a global maximum, and this maximum must
occur either at a critical point of f in the open interval (a, b) or at one of the endpoints a or b.
True
False
(d) Any local minimum or local maximum of a function f must occur at a critical point of f.

True
False
(e) Every function f defined on (-∞, 0) that satisfies the condition that lim f(x) =
lim f(x) = o must have at least
X -0
one critical point.
True
False
(f) The function f(x) = Vx is differentiable at x =
0.
True
False
(g) The function f(x) = |x| is not continuous at x = 0.
O True
False

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