Problem Set #3 – Due Thursday, Feb. 11
No calculator
Graph of f 
y


x










The continuous function f  is defined on the interval 2  x  4 . The graph of f  consists
of a quarter circle off radius 2 and three line segments, as shown in the figure above. If
f (0)  1
(a) Evaluate f (1) and f (3) .
(b) Determine the x-coordinate of the point at which f has an absolute maximum on the interval
2  x  4 . Justify your answer.
(c) Find all values of x on the interval 2  x  4 for which the graph of f has a point of
inflection. Give a reason for your answer.
(d) Find the average rate of change of ƒ on the interval 2  x  4 . Determine whether there is a
value c on the interval 2  x  4 such that f (c ) is equal to the average rate of change.
Explain.