Section 3.4- Rates of change in the Natural and Social Sciences

Equations you need to know and memorize!

Cost Function = C(x) Marginal Cost = C’(x)

Problems

Example 1:

A particle moves according to a law of motion , , where is measured in seconds and in feet.

a) Find the velocity at time

b) What is the velocity after 3

c) When is the particle at rest?

d) When is the particle moving in the positive direction?

e) Find the total distance traveled during the first 8

f) Draw a diagram to illustrate the motion of the particle.

Equation:

a)

b)

c) The particle is at rest when

d) The particle is moving in the positive direction when

e) The particle is moving in the positive direction and in the negative direction, we need to calculate the distance traveled in the intervals and separately.

and

the total distance traveled during the first 8s is 25+9=34 ft.

f)

Example 2:

The position function of a particle is given by , when does the particle reach a velocity of 5 m/s?

Since the particle reaches a velocity of 5 m/s at

Example 3:

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after

What can you conclude?

After seconds, the radius is so the area is

Example 4- Cost Function