$\"\"$

(a)

The function is $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

Since $\"\"$ , the function $\"\"$ is an even function.

$\"\"$

(b)

A function $\"\"$ has a local maximum at c if there is an open interval I containing c so that for all x in I , $\"\"$ , then $\"\"$ is called as a local maximum value of $\"\"$ .

A function $\"\"$ has a local minimum at c if there is an open interval I containing c so that for all x in I , $\"\"$ , then $\"\"$ is called as a local minimum value of $\"\"$ .

The function is $\"\"$ .

The function $\"\"$ has a local maximum value of $\"\"$ at $\"\"$ , i.e, $\"\"$ .

If $\"\"$ , then $\"\"$ is called as a local maximum value of

$\"\"$ .

Find $\"\"$ .

$\"\"$ .

Since $\"\"$ , the function $\"\"$ has a second local maximum value of $\"\"$ at $\"\"$ .

$\"\"$

(c)

The area under the graph of $\"\"$ bounded by the x - axis in the interval $\"\"$ is 1612.8 square units.

Since the function $\"\"$ is an even function, the area under the graph of $\"\"$ bounded by the x - axis in the interval $\"\"$ is also 1612.8 square units.

$\"\"$

(a) The function $\"\"$ is an even function.

(b) A second local maximum value of $\"\"$ at $\"\"$ .