(7)

Step 1:

The function is $\"\"$ and $\"\"$ .

Slope of the tangent line equation is derivative of the function.

$\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

Product rule of derivatives : $\"\"$ .

$\"\"$

$\"\"$ .

Substitute $\"\"$ in derivative of the function.

$\"\"$

Slope of the tangent line equation is $\"\"$ .

Step 2:

Find the point of tangency.

Substitute $\"\"$ in the function.

$\"\"$

Tangent point is $\"\"$ .

Step 3:

Find the equation of tangent line.

Point slope form of the line equation : $\"\"$ .

Substitute $\"\"$ and $\"\"$ in point slope form of line equation.

$\"\"$

Tangent line equation is $\"\"$ .

Solution :

Tangent line equation is $\"\"$ .

(8)

The function is $\"\"$

Differentiate $\"\"$ on each side with respect to $\"\"$ .

$\"\"$

Quotient rule of derivatives : $\"\"$ .

$\"\"$

Find the critical points.

A critical number of a function $\"\"$ is a number $\"\"$ in the domain of $\"\"$ such that either $\"\"$ or $\"\"$ does not exist.

$\"\"$ does not exist when $\"\"$

$\"\"$

The critical point is $\"\"$ .

The test intervals are $\"\"$ and $\"\"$

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

Therefore the function is increasing on the intervals $\"\"$ and $\"\"$ .

Solution :

The function is increasing on the intervals $\"\"$ and $\"\"$ .