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Calculus I                                                  Test #2                                      April 9, 2004

Name____________________             R.  Hammack                            Score ______
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(1) Use the limit definition of the derivative to find the derivative of the function .

(2) The graph of a function is shown below.  Using the same coordinate axis, sketch a graph of  .

(3) Suppose f and g are functions for which , , , and .
Suppose also that .  Find .

(4) State two things that the derivative of a function tells you.  Be specific.

(5)

(6)

(7)

(8)

(9)

(10)  If     ,    find .

(11)

(12)

(13)

(14)

(15)  Find all values of x for which the tangent line to     at   has a slope of 1.

(16)  Find the slope of the tangent line to the graph of the equation    at the point (1, 1).

(17)  Find the equation of the tangent line to the graph of at the point where .

(18)  A 10-foot ladder leans against a wall at an angle with the horizontal. The top of the ladder is y feet above the ground. If the bottom of the ladder is pushed toward the wall, find the rate y changes with respect to   when .

(19)  A 10-foot ladder leans against a wall.  If the bottom of the ladder is pushed toward the wall at a rate of 2 feet per second, how quickly is the top of the ladder moving up the wall when it's 8 feet above the floor?