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