Chapter 1.3, Problem 40E

(a)

To determine

To graph: the given function using graphing utility.

Explanation of Solution

Given information:

The given equation is $g(x)=x^3+3x^2-9x-27$

The graph of $g(x)=x^3+3x^2-9x-27$ is shown below.

  

(b)

To determine

To find: the intervals that the function is increasing, decreasing and constant.

Explanation of Solution

Given information:

The given equation is $g(x)=x^3+3x^2-9x-27$

Consider the graph of from part a.

The function is increasing on $(-\infty ,-3)\&(1,\infty )$ .

Decreasing on $(-3,1)$

constant never.

Use a table of values to verify the results:

$x$	$-5$	$-4$	$-2$	$0$	$2$	$3$
$f(x)$	$-32$	$-7$	$-5$	$-27$	$-25$	$0$
	increasing	decreasing	increasing

Hence, the results are verified using table of values.