4.6 Rates of Change

Suppose d is displacement and t is time, what does imply?

Suppose V is the volume of a balloon and t is time, what does imply?

Suppose d is displacement v is velocity and t is time, what does and imply?

A skier is coming down a hill. Suppose a is the skier's altitude and v is their velocity. Assign possible values to and .

Ex 1 The volume of air V (in) in a hot air balloon after t minutes is given by where t is the time in minutes, . Find:

(a) the initial volume.

(b) the volume at t = 8.

(c) the rate of change of the volume at t = 4. Interpret this value.

Cost Function

C(x) is a function associated with the cost of producing x items. C'(x) is called the marginal cost and represents the cost of producing the next item.

R(x) is called the revenue function and represents the money generated by selling x items. R'(x) is called marginal revenue.

P(x) is the profit function and P(x) = R(x) – C(x).

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