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Calculus I Test
#3 May
4, 2004

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) Solve the equation . (It's
OK to have logarithms in your final answer.)

(5) Simplify the following expressions as much as possible.

(a)

(b)

(c)

(d)

(6) Find the following derivatives.

(a)

(b)

(c)

(d)

(7) The graph of the
derivative of a function f(x)
is drawn. Answer the following questions about the
function f(x).

(a) Find the interval(s) on which f(x)
increases.

(b) Find the critical points
of .

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

(d) Find the intervals on
which the graph of f(x) is concave
up/down.

(8) These problems are about
the function .
Answer the following questions about f(x).

(a) Find the critical points of .

(b) Find the intervals of
increase/decrease of *f*(*x*).

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

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