   Chapter 9.5, Problem 35E ### 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

# In Problems 35 and 36,(a) find f'(x).(b) graph both f(x) and f'(x) with a graphing calculator.(c) identify the x-values where f ' ( x ) =   0 , f ' ( x )   >   0 ,  and  f ' ( x ) <   0 .(d) identify x-values where f(x) has a maximum point or a minimum point, where f(x) is increasing, and where f(x) is decreasing. f ( x ) = 10 x 2 x 2 + 1

(a)

To determine

To calculate: The derivative of the function f(x)=10x2x2+1.

Explanation

Given Information:

The provided function is,

f(x)=10x2x2+1

Formula used:

If f(x)=u(x)v(x) where u and v are differentiable functions of x, with v(x)0, then,

f(x)=v(x)u(x)u(x)v(x)[v(x)]2

Calculation:

Consider the provided function,

f(x)=10x2x2+1

Now, use the quotient rule of derivatives,

f(x)=v(x)u

(b)

To determine

To graph: The functions f(x)=10x2x2+1 and f(x)=20x(x2+1)2.

(c)

To determine

The values of x where f(x)=0, f(x)>0 and f(x)<0 if f(x)=10x2x2+1.

(d)

To determine

The values of x where f(x) has a maximum point, minimum point, increasing and decreasing.

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