   Chapter 10.1, Problem 17E ### 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 3 + x 2 2 − 2 x + 1

(a)

To determine

To calculate: The value y=f(x) of the function y=x33+x222x+1.

Explanation

Given Information:

The provided function is,

y=x33+x222x+1.

Formula Used:

The power rule of derivative,

ddx(xn)=nxn1

Where, n is any positive integer.

Constant rule of derivative,

ddx(cf(x))=cddx(f(x))

Where, c is any positive integer.

Calculation:

Consider the provided function,

y=x33+x222x+1

The first derivative of the equation is,

dydx=ddx(x33+x22

(b)

To determine

To calculate: The critical values of the function y=x33+x222x+1.

(c)

To determine

To calculate: The critical points of the function y=x33+x222x+1.

(d)

To determine

To calculate: The intervals of x-values where the function y=x33+x222x+1 is increasing and decreasing.

(e)

To determine

Whether the critical points are relative maxima, relative minima, or horizontal points of inflection for the function y=x33+x222x+1 and verify the result using graphing utility.

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