   Chapter 3.3, Problem 51E

Chapter
Section
Textbook Problem

# 51-52 Estimate the intervals of concavity to one decimal place by using a computer algebra system to compute and graph f′′. f ( x ) = x 4 + x 3 + 1 x 2 + x + 1

To determine

To estimate:

Using computer algebra system

(i) The intervals of concavity to one decimal place of fx=x4+x3+1x2+x+1

(ii) Graph f"

Explanation

1) Concept:

Use the command of MAPLE (computer algebra system) sketch the graph f" by concavity test find the interval of concavity.

2) Tests:

Concavity test:

If f"(x)>0 then the graph of f is concave upward.

If f"(x)<0 then the graph of f is concave upward.

3) Given:

fx=x4+x3+1x2+x+1

4) Calculation:

Use MAPLE (computer algebra system), to plot f"

To plot f" use the command

plot(diff(diff(f,x),x), x=-2..2);

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