help? product rule or quotient rule

Question

Answer 1

(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 .

Answer 2

(8)

Step 1 :

The function is .

Differentiate on each side with respect to .

Quotient rule of derivatives : .

.

Step 2 :

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 .