Calculus Qs

Derivatives of Polynomials

1. Find the equation of the line tangent to

at the point where

2. For the above function, what does the derivative at tell you

about the direction at that point? Is it increasing, decreasing, or neither? Why?

3. For the function ,

a. Sketch the graph of

b. Give the local extrema (peaks and valleys; maximum and minimum) for

4. If a company’s sales (in millions of dollars) for time months is given by

a. Find

b. Find

c. What does this tell you about the company’s position in the month of

May (i.e., )?

5. If the derivative can be thought of as a marginal revenue function for x units (in hundreds of items) sold, and the revenue for a company is given by the function

,

a. Sketch the graphs of the functions and

b. Find the number of units sold at which the marginal revenue begins to increase.

1

6. The altitude (in feet) attained by a model rocket t seconds into flight is given by the function

a. Find the maximum altitude attained by the rocket.

b. Why does it not make sense to use this function after

seconds? Use the graph of

h (t)

1 3 2

that is given.

h (t)

3

t 4 t 250

200

150

100

50

20 t 2, for t 2.

t

-8 -6 -4 -2 2 4 6 8 10 12 14 16 18

-50

2