   Chapter 10.1, Problem 20E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# For each function in Problems 15-20(a) find y '   =   f ' ( x ) . (b) find the critical values.(c) find the critical points.(d) find intervals of x-values where the function is increasing and where it is decreasing.(c) classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing calculator. y = − ( x − 3 ) 2 / 3

(a)

To determine

To calculate: The value y=f(x) of the function y=(x3)23.

Explanation

Given Information:

The provided function is y=(x3)23.

Formula Used:

In order to differentiate a function y=f(x),

The differentiation must be initiated on both sides with values corresponding to the power rule, that is:

dydx=ddx(f(x))y=f(x)

As per the power rule,

ddx(xn)=nxn1

Calculation:

Consider the provided function y=(x3)23,

Take out the first derivative of the equation y=(x3)23 with respect to x:

dyd

(b)

To determine

To calculate: The critical values of the function y=(x3)23.

(c)

To determine

To calculate: The critical points of the function y=(x3)23 by using the original function.

(d)

To determine

To calculate: The intervals of x-values where the function y=(x3)23 is increasing and where it is decreasing.

(e)

To determine

To calculate: The relative maxima, relative minima, or horizontal points of inflection by observing the graph y=(x3)23.

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