Let f(x) = k ln(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 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 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 f has a local extreme value, and classify this extrema as a local maximum or minimum. Justify your answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff42c59a5-908c-4bcd-9e36-90d243a82d72%2Fda2e5432-bd95-45b7-af55-38c896eb753e%2F7kvs5x9_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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