x xg

1.

For problems #1 and #2, sketch the slope field. Sketch the graph of y  f x  that goes through the



2.





point (3,2). 1.

f x  

2.

f x   x 2  2 x  3

1 x 1 2

For each of the following functions find: A. g  x  B. g 4 C. g x  D. g 4  3.

g x   x 3  3x 2  5 x  2

4.

































































E. Explain what the sign of g 4  tells you.

g x  

1 x3

5.

g x  

x

For each of the following functions, find an equation for the line tangent at the given x-value. 1 6. f x   x 3  2 x 2  5 x  3 tangent at x  2 7. r x   2  3x tangent at x  1 x

For each of the following functions: A. Find all critical x-values B. Find all increasing intervals

8.

1 5 y  x3  x 2  7 3 2

9.

y  x2  6x  2

C. Find all decreasing intervals

10.

y  2x  5

For each of the following, evaluate the given definite integral, showing all work: 5

11.

 x  4dx 2

 x 4

12.

2

2



 x  2 dx

13

13.

 6dx 3

