BC 2,3
Problem Set #4
(Due Thursday, October 10)
Name: ______________
Please show appropriate work. Work should be shown clearly, using correct mathematical notation.
Please show enough work on all problems so that others could follow your work and do a similar
problem without help. Collaboration is encouraged, but in the end, the work should be your own. A
calculator/computer will be required for parts of problem 2; you may do any integrals without
showing work, but show all set-up carefully.
1.
(1999 BC #5):
Graph of f
The graph of the function  shown at the right
consists of three line segments. Let
 (t) dt .
x
g ( x) 
1
a.
Compute g(4) and g(–2).
b.
Find the instantaneous rate of change of g, with respect to x, at x = 1.
c.
Find the absolute minimum value of g on the closed interval [–2, 4]. Justify your answer.
d.
The second derivative of g is not defined at x = 1 or x = 2. Which of these values, if any, are
x-coordinates of points of inflection of the graph of g? Justify your answer.
BC 2,3
Problem Set #4
(Due Thursday, October 10)
Name: ______________
2. Let r  2  4cos( ) .
a. Carefully and accurately sketch the graph of r  2  4cos( ) .
b. Find the width of the inner loop of this limacon. This is the maximum vertical distance from
the bottom to the top of the loop. Round answer to nearest tenth.
c. Find the area of the region inside the larger loop and outside the inner loop.