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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?