Name                                                      :
Group (circle one) 1           2
Math 131 A candy bar quiz 3,
Tom Linton, March 3, 2000
  1. Let h(t) be the height, above ground level (in feet) of a hot air balloon, t minutes after takeoff. In common everyday language, what do the following statements tell you?
    1. h(75) = 100.








    2. h'(75) = -5.








  2. Values of the function g(x) are given in the table below. Estimate g'(2) from the values in the table.
x g(x)
1.95 -5.921
2.00 -6.468
2.05 -6.969

 
 
 
 
 
 







 
 
 

  1. A graph of the function f(x) is shown below. Use the graph to answer the following questions.
    1. At which x-value(s) does f '(x) = 0?







    2. Estimate f '(1).














    3. Is the derivative, f '(x), increasing or decreasing at x = 1? How do you know?








  1. For each description of the behavior of the derivative h'(x) below, provide a description (or plot) of the behavior of h(x) (for the same values of x). For example, if h'(x) is positive near x = 2, then h(x) is increasing at x = 2.
    1. h'(x) decreases through the x-axis at x = 2.3 (like the plot of f(x) above).










    2. h'(5) = 12 and the graph of h'(x) has a hilltop (local max) at x = 5.











    3. h'(x) is negative and increasing near x = 4.