   Chapter 3.6, Problem 13E

Chapter
Section
Textbook Problem

# If f is the function considered in Example 3, use a computer algebra system to calculate f ' and then graph it to confirm that all the maximum and minimum values are as given in the example. Calculate f " and use it to estimate the intervals of concavity and inflection points. f ( x ) = x 2 ( x + 1 ) 3 ( x − 2 ) 2 ( x − 4 ) 4

To determine

To estimate:

The intervals of concavity and inflection points, to confirm the values of maximum and minimum by using graph.

Explanation

1) Given:

fx=x2x+13x-22x-44

2) Calculation:

Given function is fx=x2x+13x-22x-44

Therefore, the derivative of the function is

f'x=xx+12(x3+18x2-44x-16)x-23x-45

Graph of f’(x)

From the graph, it is observed that the extreme points occurred at -20.145, -0.322 and 2.467

Now calculate

f''x=(x+1)(x6+36x5+6x4-628x3+684x2+672x+64)x-24x-46

Graph of f''x

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