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Consider the function f(x) = sin(xª(1 – x)') with a, b > 0. We know that: %3D f is differentiable at 0 regardless of a, b > 0. f has at least one critical point in the interval [0, 1].

Consider the function f(x) = sin(xª(1 – x)') with a, b > 0. We know that: %3D f is differentiable at 0 regardless of a, b > 0. f has at least one critical point in the interval [0, 1].

College Algebra (MindTap Course List)
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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Consider the function f(x) = sin(xª(1 – x)') with a, b > 0. We know that: f is differentiable at 0 regardless of a, b > 0. f has at least one critical point in the interval [0, 1]. f has an absolute maximum in the interval [0, 1] at x = 0. f has an absolute minimum in the interval [0, 1] at x = 1.
Transcribed Image Text:Consider the function f(x) = sin(xª(1 – x)') with a, b > 0. We know that: f is differentiable at 0 regardless of a, b > 0. f has at least one critical point in the interval [0, 1]. f has an absolute maximum in the interval [0, 1] at x = 0. f has an absolute minimum in the interval [0, 1] at x = 1.
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