AP Calculus AB
Section 2.1-2.2 Worksheet
Name ________________________
Date ______________Period _____
Find the slope of the line tangent to the graph of the function at the given point. (Use the limit process to find the
derivative).
1.
f ( x) 2 5x;
1,7
2, 4
2.
g ( x) 8 x2 ;
4.
f ( x) 5 x 2 5 x 8
Find the derivative of the function by the limit process.
3.
h( x ) 5
6
x
7
Write the equation of the line tangent to the graph at the given point. (Shortcuts are acceptable).
5.
f ( x) x2 7 x 4;
4, 8
6.
f ( x) 2 x ;
9, 6
Match the graph of the function to its derivative.
7.
Find the derivative of the function.
8.
f ( x) x 3
9.
f ( x)
1
x8
10.
g ( x) x 5 5 x 3
11.
f ( x) 6 x3 6 x 2 2
12.
f ( x) 6 x 2 4cos x
13.
f ( x) 3x3 2sin x
14.
2
f ( x) 7 5cos x
x
15.
x4 6
f ( x)
x3
Determine all points, (if any), at which the graph of the function has a horizontal tangent.
16.
y x3 12 x 2 1
17.
y x4 4x 5
Answer the following questions.
18. A ball is thrown straight down from the top of a 210-ft building with an initial velocity of -24 ft per second. The
position function is s (t ) 16t 2 vot so . What is the velocity of the ball after 1 second?
19. A projectile is shot upwards from the surface of the earth with an initial velocity of 148 meters per second. The
position function is s (t ) 4.9t 2 vot so . What is its velocity after 4 seconds?
20. Find the average rate of change of y with respect to x on the interval 2, 2 , where y 3x 2 2 x .
21. Create a sign chart to show intervals on which the function is increasing/decreasing and on which the derivative is
positive/negative. Sketch the graph of the derivative on the same set of axes as the function.
a
b
Answers:
1.
2.
-5
-4
6
7
4. 10 x 5
5. y 8 x 4
3.
6.
y 6 9 x 9
7. A
8. f '( x) 3x 2
8
x9
10. g '( x) 5 x 4 15 x 2
9.
f '( x)
11. f '( x) 18 x 2 12 x
12. f '( x) 12 x 4sin x
13. f '( x) 9 x 2 2cos x
2
14. f '( x)
7x
6
7
5sin x
18
x4
16. 0,1 and 8, 257
15. f '( x) 1
17. 1, 2
18.
19.
20.
21.
-56 ft/s
108.8 m/s
-2
Graph
0
