   Chapter 10.3, Problem 3E ### 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 1-6, find the absolute maxima and minima for f ( x ) on the interval [ a ,   b ] . 3. f ( x ) = x 3 + x 2 − x + 1 , [ − 2 , 0 ]

To determine

To calculate: The absolute maxima and minima for f(x)=x3+x2x+1 in the interval [2,0].

Explanation

Given Information:

The provided function is:

f(x)=x3+x2x+1

Formula used:

If f(x) and g(x) are two differentiable functions then by the property of derivative:

ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

And

ddxxn=nxn1

Where n is a constant and x is the variable.

Calculation:

The absolute maxima and absolute minima will occur only at the critical points. To calculate the critical points of the provided function find the first derivative of the function:

f(x)=x3+x2x+1f'(x)=ddx(x3+x2x+1)

Use ddx(f(x)+g(x))=ddxf(x)+ddxg(x)

f'(x)=ddxx3+ddxx2ddxx+ddx1

Now use ddxxn=nxn1

f'(x)=ddxx3+ddxx2ddxx+ddx1=3x2+2x1+0=3x2+

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