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Let f(x) = k ln(x² + 3) + 5, where k < 0. Do the following. (a) Find the critical numbers of f, and make a sign chart for f'(x). (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. Justify each answer. (c) Find the value of x where f has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.

Let f(x) = k ln(x² + 3) + 5, where k < 0. Do the following. (a) Find the critical numbers of f, and make a sign chart for f'(x). (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. Justify each answer. (c) Find the value of x where f has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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Let f(x) = kln(x² + 3) + 5, where k < 0. Do the following. (a) Find the critical numbers of ƒ, and make a sign chart for f'(x). (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. Justify each answer. (c) Find the value of x where ƒ has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.
Transcribed Image Text:Let f(x) = kln(x² + 3) + 5, where k < 0. Do the following. (a) Find the critical numbers of ƒ, and make a sign chart for f'(x). (b) Find the open interval(s) on which f is increasing and the open interval(s) on which f is decreasing. Justify each answer. (c) Find the value of x where ƒ has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.
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