Math 165

Spring 2001

Exam 2

 

  1. (30 pt) Compute the derivatives of the following functions:

a)            b)           

 

c) d)  e)

 

  1. (10 pt) Use implicit differentiation to find the tangent line to the curve defined by  at the point

 

  1. (15 pt) For the following function, find all critical points and then find the maximum and minimum values of the function on the interval [0,3]:

.

 

  1. (15 pt) Find the maximum and minimum values of the function  on the interval

 

  1. (15 pt) You are standing on a long straight beach. Off the coast is located a lighthouse which has a beam that make 1 revolution every 3 seconds. Additionally assume that you are standing on the point on the beach closest to the lighthouse and that the lighthouse is 4 miles away. How fast is the beam of light moving towards you down the beach at the instant that it is 4 miles away from you?

 

  1. (10 pt) Let , find a formula for

 

  1. (15 pt) You have a circular drum whose height and base diameter are equal. You measure the height and find it to be 5 feet with an error of ± 0.5 inches. Estimate the maximum error obtained by using this measurement to compute the volume of the drum. Also compute the relative error.