Math 115

Practice Exam 2

November 2003

 

  1. Use the linear approximation to estimate .

 

  1. You are using Newton’s formula to estimate the root of x3 – 3x +  1. If x5 = 0.2, what is x6?

 

 

  1. Find the absolute maximum and minimum value of the function f(x) = x 4 – 8x2 +1 on the interval [-1,3].
  2. For the function f(x) =   

 

give the intervals where f is increasing-decreasing, concave up-down, list the inflection points and local maxima and minima (Use either the first or second derivative test to justify your answer).

  Same thing for f(x) = x3 – 6x2 – 20x + 2.

 

  1. A farmer wishes to fence in a rectangular pasture with one side bounded by a straight river bank. He wants to divide the pasture in half with a length of fence running parallel to the river. If he has 2000 feet of fencing, what is the maximum total area he can enclose.

Other sample problems : p. 306 – 9,14,20,22

 

  1. Sketch a graph of f(x) = x/(x-1). Include the details listed by the text.

 

  1. Find the antiderivatives:  (a)   3x + 4,  (b) 5sec 2x  (c) e-x + cos(x)  (d)   x-1 + x-2

 

  1. State the Mean Value Theorem. Find the point c guaranteed by the Mean Value Theorem for f(x) = 4x – 1/x on the interval [1,2]. What if the interval is [-1,1]?

 

  1. Use L’Hopital’s rule or some other rule to find the limits:

 

((a)                          (b)