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

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...
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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
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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