help? -(-derivatives -trig-functions-exponential logs-)

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 on each side with respect to .

Slope of the tangent at .

Slope of the tangent line at is .

Step 2:

Find the point of tangency.

Substitute in the funtion.

Point of tangency is .

Step 3:

Slope point form of the equation is .

Substitute and slope in the point slope form.

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.

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

Equate to zero.

Apply logarithm on each side.

Critical points is .

Comments

Contd..

Step 2:

The test intervals are and .

Therefore the function is increasing on the interval .

The function is decreasing on the interval .

(a)

is in the interval of .

Hence the function is decreasing at .

(b)

is in the interval of .

Hence the function is decreasing at .

(c)

is in the interval of .

Hence the function is increasing at .

Solution:

(a) The function is decreasing at .

(b) The function is decreasing at .

(c) The function is increasing at .