Question attached to image 6:14 PM Thu Nov 565%T+ :1.) Find the critical points of the function. Give answer asofalistnumbers.2gex>= ?qgexs=メ-12

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Description: Question attached to image 6:14 PM Thu Nov 565%T+ :1.) Find the critical points of the function. Give answer asofalistnumbers.2gex>= ?qgexs=メ-12

Answered: O Find the critical points of the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 5T

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6:14 PM Thu Nov 5
65%
T
+ :
1.) Find the critical points of the function. Give answer as
of
a
list
numbers
.2
gex>= ?q
gexs=
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1
2

Expert Solution

Given data,

The function is $g (x) = \sqrt[3]{x^{2} - 9}$ .

Step 1

This equation is in factored form, it means x and y intercepts the graph.

The x intercept are $\pm 3 and 0$ when y is 0.

So, the interval of x is $- 3 \leq x \leq 3$ .

Taking the given function as,

$g (x) = \sqrt[3]{x^{2} - 9} = {(x^{2} - 9)}^{\frac{1}{3}}$

The derivative of the function with respect to x is,

$\frac{d}{d x} g (x) = \frac{d}{d x} {(x^{2} - 9)}^{\frac{1}{3}} g' (x) = \frac{1}{3} {(x^{2} - 9)}^{- \frac{2}{3}} \times \frac{d}{d x} (x^{2} - 9) g' (x) = \frac{1}{3} 2 x {(x^{2} - 9)}^{- \frac{2}{3}}$

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