Calculus I 
Test #2

November 1, 2002

Name____________________ 
R. Hammack

Score ______

(1) (25points)
(a) State the limit definition of .
(b) State two of the three main interpretations of a derivative . Be
specific.
(c) Use the limit definition from Part a to find the derivative of .
(d) Use the derivative rules to find the derivative of
without using a limit. (Answer should agree with Part c.)
(e) Find the equation of the tangent line to
at the point .
(2) (20 points) The problems on this page concern the function that is graphed below.
(a) Using the same coordinate axis, sketch the graph of .
(b) For which value(s) of x is
increasing most rapidly?
(c) For which value(s) of x is
greatest?
(d) For which value(s) of x is
decreasing most rapidly?
(e) For which value(s) of x is
smallest?
(f) Suppose . Estimate
.
(g) Suppose . Estimate
.
(3) (35 points) Find the derivatives of the following functions.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(5) (10 points) Find by
implicit differentiation:
(6) (10 points) A rocket, rising vertically, is tracked by
a radar station that is on the ground 5 miles from the launchpad. How
fast is the rocket rising when it is 4 miles high and its distance from the
radar station is increasing at a rate of 2000 miles per hour?