$\"\"$

(a)

The function is $\"\"$ , $\"\"$ .

Apply first derivative with respect to $\"\"$ .

$\"\"$

Apply second derivative with respect to $\"\"$ .

$\"\"$

(b)

If we have to find out the relative extrema by equating $\"\"$ .

$\"\"$

Using graphing utility relative extremas are $\"\"$ and $\"\"$ .

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

$\"\"$ .

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

$\"\"$ .

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

$\"\"$ .

The relative extrema points are $\"\"$ , $\"\"$ and $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

To determine the points of inflection, equate $\"\"$ .

$\"\"$

Using graphing utility inflection points are $\"\"$ and $\"\"$ .

Therefore inflection points are $\"\"$ and $\"\"$ .

$\"\"$

(c)

Sketch the function $\"\"$ , $\"\"$ and $\"\"$ .

$\"\"$

(a) $\"\"$ .

$\"\"$ .

(b)

The relative maximum is $\"\"$ .

Inflection points are $\"\"$ and $\"\"$ .

(c)

$\"\"$ .