help-derative

Question

Answer 1

(7)

Step 1:

The function is .

Find the tangent line equation at .

Slope of the tangent line is the first derivative of the function at .

Apply derivative with respect to .

Slope of the tangent at .

Step 2:

Find the point of tangency.

So the point of tangency is .

Step 3:

Slope point form of the equation is .

Substitute point and slope .

Solution:

The tangent line equation at is .

Answer 2

(8)

Step 1:

The function is .

Differentiate on each side with respect to .

Find the critical points.

Since it is a polynomial it is continuous at all the point.

Thus, the critical points exist when .

Equate to zero.

The critical points are and .

Step 2:

The test intervals are .

Therefore the function is increasing on the intervals and .

The function is decreasing on the interval .

Solution :

The function is increasing on the intervals and .

The function is decreasing on the interval .