Name_______________
MAC 2233 Exam 2 Part 1
You are not permitted to use a calculator for this portion of the exam. When you have
finished answering these questions, hand in this sheet to obtain the second portion of the
exam. You must provide complete answers to the questions. Correct answers without
supporting work will receive minimal credit.
Use the graph on the right to answer questions 1 and 2.
1. For which x-values will f ( x)  0 ?
2. For which x-values will f (x) be undefined?
3. Find all values of x (if any) where the tangent line to the graph of y  3x 2  x is
horizontal.
4. Find f (x) for f ( x)  3(7) x  2 .
5. Find f (x) for f ( x)  log 4 (2x  1) .
Name_______________
MAC 2233 Exam 2 Part II
For this portion of the exam, you are permitted to use a graphing calculator. You must
answer each question completely. Correct answers without supporting work will receive
minimal credit.
1. Use the limit definition of the derivative to find f (x) for f ( x)  x 2  2 x  3 ?
2. Find f (x) for f ( x)  4 x 5  3x 4  2 x 2  x  8 .
3. Find f (x) for f ( x) 
2 x 8 x1.5
4

 2.4 .
5
3
3x
4. Find f (x) for f ( x)  3 x  3
5. Find f (x) for f ( x) 
5
x
.
2x  1
.
5x  8
6. Find f (x) for f ( x)  (4 x 2  3) 5 .
7. Find f (x) for f ( x)  3 3  2 x 2 .
 5x 3 
 .
8. Find f (x) for f ( x)  ln 
 x  2
9. Find f (x) for f ( x)  e x .
2
10. Find f (x) for f ( x)  ln | 2 x  3 | .
11. Find f (x) for f ( x)  (3x  1) 2 e x .
12. If C ( x)  10 x  3 and R( x)  40 x  0.6 x 2 , find the marginal profit function.
13. Assume that the demand function for bubble-jet printers is given by p = 170 -
x
,
100
where p is the price of a single printer, and x is the number of printers that can be
sold at price p in one month. Calculate the marginal revenue at a demand level of
500 printers per month. Interpret your results.
14. Find the equation of the tangent line to f ( x) 
1
at x  1.
x2
15. An offshore oil well is leaking oil and creating a circular oil slick. If the radius of the
slick is growing at a rate of 2 miles/hour, find the rate at which the area is increasing
when the radius is 3 miles. (The area of a disc of radius r is A  r 2 ).