help? functions and derivatives?

Question

Answer 1

13)

The given function is

Find the derivative with respect to x.

Find the slope of the tangent at x = 1.

Find the point of the tangent on the curve.

Substitute x = 1.

The point is (1 , 4).

Find the tangent equation by using the formula.

Substitute m = 2 and .

Therefore, the equation of the tangent is .

Answer 2

(14)

Step 1:

The position function is .

Find the velocity at time .

Apply derivative on each side with respect to .

Apply power rule of derivatives  .

.

The velocity of the object at time is .

Solution:

The velocity of the object at time is .

Answer 3

(15)

Step 1:

The velocity of the object at time is .

If the object stops, then the velocity of the object becomes zero.

In this case the velocity of the object never becomes zero.

, for all values of .

Therefore, the object never stops moving.

Solution:

The object never stops moving.