Name _____________
Period ____
Honors Brief Calc.
Semester 2 Final Exam Review #1
1. lim f ( x) 
x2
2. For all values of x, f ' ( x)  0 and f ' ' ( x)  0 , draw a curve that could represent a part of
the graph of f.
3. Find the slope of the tangent line f ( x)  x 2  x when x = 3
4. Find the area enclosed by f ( x)  x 2 and g ( x)  x
5. The relationship between profit P of a firm and the selling price x of its goods is
P  500 x  10 x 2 . What selling price is required to generate a maximum profit?
6. Find the local maximum of y  x 4  4x 3
7. If f ' ( x)  x 6  x , find f (x)
4
8. Evaluate
1
 2 x dx
1
9. Integrate by parts
 xe dx
x
10. If y  4 x 2  2 x  5 then
dy
at x = 2 is
dx
11. If f ( x)  (4 x  3) 5 then find f ' ' ( x)
12. Evaluate  (4 x 3  6 x  2)dx
13. Write (but do not solve) the integral that expresses the area of the region bounded by the
graphs of x  0 , x  4 , and y  x 2
14. Find the value of lim
x 1
15. Find
x2  x  2
x2 1
d x3 3
e
dx
16. Solve the differential equation
dy
 x 2  x using the boundary condtion y = 5 and x = 3.
dx
c
17. For n  1,  x n dx equals
a
18. For which value does the limit not exist?
19. Use implicit differentiation to find
dy
if xy  5 x  7
dx
20. Find the limit: lim
x 1
x2 1
x 1
21. Let C(x) be the cost function in dollars of producing x units. Let R(x) be the revenue
function for selling x units. Write the equation that would be needed to determine how
many units should be sold to maximize profit?
22. Evaluate
x
2
x 3  5dx
( x  h) 2  x 2
23. Find lim
at the point x = 3
h 0
h
24. If y  cos( x 3 ) , find y '
25. If f ( x) 
x2  2
, find f ' ( x)
x3