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.

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