For each of the questions below, indicate if the statement is true (T) or false (F). (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 f 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 (-∞, ∞) that satisfies the condition that lim f(x) =_lim_ f(x) = ∞o must have at least x-00 one critical point. True False (f) The function f(x)=√x is differentiable at x = 0. True False (g) The function f(x) = |x| is not continuous at x = 0.
For each of the questions below, indicate if the statement is true (T) or false (F). (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 f 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 (-∞, ∞) that satisfies the condition that lim f(x) =_lim_ f(x) = ∞o must have at least x-00 one critical point. True False (f) The function f(x)=√x is differentiable at x = 0. True False (g) The function f(x) = |x| is not continuous at x = 0.
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 98E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
Related questions
Question
![For each of the questions below, indicate if the statement is true (T) or false (F).
(a) Any critical point of a function f is either a local maximum or local minimum for f.
O True
False
(b) Every differentiable function is continuous.
True
False
(c) Any function f 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.
O True
False
(d) Any local minimum or local maximum of a function f must occur at a critical point of f.
O True
False
(e) Every function f defined on (-∞0, ∞o) that satisfies the condition that lim f(x) = lim f(x) = ∞o must have at least
x-00
x--00
one critical point.
True
False
(f) The function f(x)=√x is differentiable at x = 0.
True
O False
(g) The function f(x)= [x] is not continuous at x = 0.
True
O False
00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2d79032-32db-4435-bc8c-34ca2691b1b6%2F2838f726-7b6b-4493-8889-f494a1c5b165%2Ft36tfvf_processed.png&w=3840&q=75)
Transcribed Image Text:For each of the questions below, indicate if the statement is true (T) or false (F).
(a) Any critical point of a function f is either a local maximum or local minimum for f.
O True
False
(b) Every differentiable function is continuous.
True
False
(c) Any function f 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.
O True
False
(d) Any local minimum or local maximum of a function f must occur at a critical point of f.
O True
False
(e) Every function f defined on (-∞0, ∞o) that satisfies the condition that lim f(x) = lim f(x) = ∞o must have at least
x-00
x--00
one critical point.
True
False
(f) The function f(x)=√x is differentiable at x = 0.
True
O False
(g) The function f(x)= [x] is not continuous at x = 0.
True
O False
00
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