Chapter 4.4, Problem 60E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Finding Extrema and Points of Inflection Using Technology In Exercises 59-62, use a computer algebra system to analyze the function over the given interval, (a) Findthe first and second derivatives of the function, (b) Find any relative extrema and points of inflection, (c) Graph f, f' and f " on the same set of coordinate axes and state the relationship between the behavior of f and the signs of f' and f”. f ( x ) = x 2 6 − x 2 , [ − 6 , 6 ]

(a)

To determine

To calculate: The First two derivatives of the function f(x)=x26x2 over the interval [6,6].

Explanation

Given:

The function f(x)=x26âˆ’x2 over the interval [âˆ’6,6].

Formula Used:

Calculation:

Differentiate the provided function.

f'(x)=2x6âˆ’x2+x2(âˆ’2x)26âˆ’x2=2x(6âˆ’x2)âˆ’x36âˆ’x2=12xâˆ’3x36âˆ’x2

Now differentiate the first derivative to obtain the second derivative:

f''

(b)

To determine

To calculate: The relative extremas and the points of inflection.

(c)

To determine

To graph: The function f, f' and f'' on the same coordinate axis.

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