help-diff

Question

Answer 1

(5)

Step 1:

The function is and point is .

Apply derivative on each side with respect to x.

The derivative of the function represents the slope of the tangent line.

Find the slope of the tangent line at a point .

Substitute in .

Therefore the slope of the tangent line is .

Step 2:

Find the tangent line equation at a point .

Point - slope form of a line equation : .

Substitute and in point - slope form.

Therefore the tangent line equation is .

Solution :

Therefore the tangent line equation is .

Answer 2

(6)

Step 1:

The function is and point is .

Differentiate on each side with respect to .

Find the critical points.

The critical points exist when .

Equate to zero.

The critical point is .

Step 2:

Rewrite the function.

The test intervals are and .

The function is increasing on the interval .

The function is decreasing on the interval .

The point is .

The point lies on the interval .

Therefore the function is increasing at the point .

Solution :

The function is increasing at the point .