Which of the following statements is TRUE? a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c•d. O b. The critical points of f' (x) are same as the critical points of f(x) The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. C. d. All of the statements are false. e. Every local maximum is a global maximum
Which of the following statements is TRUE? a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c•d. O b. The critical points of f' (x) are same as the critical points of f(x) The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. C. d. All of the statements are false. e. Every local maximum is a global maximum
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed
interval [a, b], and f(x) attains its global maximum at x = c and g(x)
d, then the function f(x) · g(x)
attains its global maximum at x =
attains its global maximum on [a, b] at x = c ·
·d.
b. The critical points of f' (x) are same as the critical points of f(x)
c. The global maximum value of a differentiable function f(x) on a closed
interval [a, b] must occur at a critical value or an endpoint.
d. All of the statements are false.
e. Every local maximum
a global maximum](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81ea85b3-54ec-4a46-b00f-6f3e5cda85a0%2Fc0a96711-ad43-42b0-a4f9-8cead8efcb81%2F34qh4sc_processed.png&w=3840&q=75)
Transcribed Image Text:Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed
interval [a, b], and f(x) attains its global maximum at x = c and g(x)
d, then the function f(x) · g(x)
attains its global maximum at x =
attains its global maximum on [a, b] at x = c ·
·d.
b. The critical points of f' (x) are same as the critical points of f(x)
c. The global maximum value of a differentiable function f(x) on a closed
interval [a, b] must occur at a critical value or an endpoint.
d. All of the statements are false.
e. Every local maximum
a global maximum
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