November 1, 2002
(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.
(5) (10 points) Find by
(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?