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Calculus I                                                                     Test #3                                          November 24, 2003

Name____________________                              R.  Hammack                                             Score ______
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(1)  Sketch the graph of the function .

(2) Find the inverse of the function .

(3) Does the function    have an inverse? Explain.

(4) The graph of a one-to-one function is given.  Using the same coordinate axis, sketch the graph of .

(5) The function is invertible.  Find the number a for which .

(6) Solve the equation   .  Hint: Notice that this has the form of a quadratic.

(7)
(8)

(9)

(10)

(11) Use logarithmic differentiation to find the derivative of the function .

(12)

(13)

(14)

(15)

(16)

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(17) Find the intervals of increase/decrease.

(18)  Find the critical points of .

(19)  Find the locations of the relative extrema of , and identify them as relative maxima or minima.

(20)  Find the intervals on which the graph is concave up/down.