$\"\"$

(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 $\"\"$ .

$\"\"$

$\"\"$ and $\"\"$

$\"\"$

So the critical values of $\"\"$ .

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

Then, $\"\"$

$\"\"$

The point is $\"\"$ .

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

Then, $\"\"$

$\"\"$

The point is $\"\"$ .

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

Then, $\"\"$

$\"\"$

The point is $\"\"$ .

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

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

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

$\"\"$

The roots of above expression is $\"\"$ .

The possible points of inflection occur at $\"\"$ and $\"\"$ .

$\"\"$

(c)

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

$\"\"$

(a) $\"\"$ .

$\"\"$ .

(b)

The relative maximum in $\"\"$ and $\"\"$ .

The relative minimum in $\"\"$ .

The points of inflection occur at $\"\"$ and $\"\"$ .

(c)

$\"\"$ .