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Calculus I Test
#3 November
25, 2002

Name____________________ R. Hammack Score
______

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(1) The following function is one-to-one.
Find its inverse.

(2) Decide if the function
is invertible. Explain your reasoning.

(3) Solve the equation for
x.

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

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(5) The graph of the derivative
of a function
is sketched.

Answer the following questions about .

(a) Find the interval(s)
on which f is
increasing.

(b) Find the interval(s)
on which f is
concave down.

(c) List the x-coordinates
of all inflection points of f.

(d) List all the critical
numbers of f.

(e) List the x-coordinates
of the relative minima of f (if
any).

(6) Find the following derivatives.

(a)

(b)

(c)

(d) =

(7) Consider the function

(a) Find all the critical numbers of
f.

(b) Find the locations of all the relative
extrema of f, and classify them as
relative maximums or minimums.

(8) A formula from physics states that
an object which is propelled up or down with an initial velocity of feet
per second from a height of feet
has a height of
feet at time t seconds.

Suppose you are on top of a 48 foot tall building and toss a ball straight up
with an initial velocity of 32 feet per second. (Assume the ball is 48 feet
above the ground when it leaves your hand.)

(a) When does the object reach its highest
point?

(b) When does the object strike ground?

(c) What is the object's velocity at
the instant it strikes the ground?

(d) When does the object have a velocity
of 8 feet per second?