BC 1-2
Practice Quiz
Name: ________________
Show all appropriate work clearly for full credit. NO CALCULATORS
Skills:
1. Determine the coordinates of point P on the graph of y  1  x 2 and having positive xcoordinate that is closest to the origin.
2. Find the absolute maximum and minimum values of f ( x)  x 2e x on the interval  3,1 .
3. Ten thousand pounds of beef in cold storage are worth sixteen cents a pound. If the price
increases steadily at one cent per week while the beef loses one hundred pounds each
week in weight, and the storage costs sixty dollars a week, how long should the beef be
held before selling in order to sell for the maximum value?
4. Suppose  is the function shown at the
right.
a.
Graph of f
 
If p  x   x  f x 2 , is p  x  increasing or
decreasing at x  1 ? Justify your answer
clearly and completely.
b.
 
If p  x   x  f x 2 , is p  x  concave up or concave down at x  1 ? Justify your answer
clearly and completely. You may assume that the graph of f has points of inflection at
x  0.8 and x  1.5 .
BC 1-2
Practice Quiz
Name: ________________
Concepts:
6. Suppose that f is a continuous function on the interval [a, b] . Prove that there is a fixed
point in the interval; that is, there exists c  [ a, b] such that f (c)  c .
7. Suppose f is defined on [0,1] , and achieves both a maximum and a minimum on [0,1] .
(a) Must  f ( x)  achieve a maximum on [0,1] ? Why or why not?
2
(b) Must  f ( x)  achieve a minimum on [0,1] ? Why or why not?
2
(c) Do your answers to (a) and (b) change with the additional assumption that f is
continuous? Why or why not?