H Calculus Name: ______
Final Exam Review Packet (Page 3)
Derivative Review
Find the derivative of each function.
1. 2. 3.
4. 5.
6. 7. 8.
]
H Calculus Name: ______
Final Exam Review Packet (Page 4)
I. Derivative Formulas for Trig.
A.
B.
C.
D.
E.
F.
Find the derivative of each function.
1. 2. 3.
4. 5. 6.
Find
1.
2.
3. Find and then determine the slope of the curve at (1,1) if
4. Find in terms of x and y if
5. Find an equation of the normal line to at (-3,4)
H Calculus Name: ______
Final Exam Review Packet (Page 5)
Related Rates Section
6. A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius of the balloon increasing at the instant the radius is 2 feet?
7. A conical tank (with the vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep.
8. A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top moving down the wall when the base of the ladder is 15 feet from the wall?
9. A boat is pulled in by means of a winch on the dock 12 feet above the deck of the boast. The winch pulls in rope at the rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out.
10. A baseball diamond has the shape of a square with sides 90 feet long. A player 30 feet from third base is running at a speed of 28 feet per second. At what rate is the player’s distance from home plate changing?
11. A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When he is 10 feet from the base of the light, at what rate is the length of his shadow changing? At what rate is the tip of his shadow changing?
12. A balloon rises at the rate of 10 feet per second from a point on the ground 100 feet from an observer. Find the rate of change of the angle of elevation of the balloon from the observer when the balloon is 100 feet above the ground?
H Calculus Name: ______
Final Exam Review Packet (Page 6)
Find the intervals for which f(x) is a) increasing b) decreasing c) concave up d) concave down. Identify the locale of all e) relative minima and f) maxima and all g) points of inflection and h) graph.
1. 1.a.______
b. ______
c. ______
d. ______
e. ______
f. ______
g. ______
2. 2. a. ______
b. ______
c. ______
d. ______
e. ______
f. ______
g. ______
Find a) the absolute maximum and b) the absolute minimum for each function over the given closed interval.
3. 3. a)______
b) ______
4. 4. a)______
b) ______
H Calculus Name: ______
Final Exam Review Packet (Page 7)
Integration Section
For problems 1 – 18, evaluate each of the indefinite integrals:
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
Determine the indefinite integral of the following:
1.
2.
3.
4.
Determine the particular solution given the following:
5.
6.
Determine the definite integral of the following:
7.
8.
9. As you drive along the highway, you step hard on the accelerator to pass a truck. Assume that your velocity, v(t) feet per second is given by where t is the number of seconds since you started accelerating. Find an equation for D(t), your displacement from the starting point, that is, from D(0)=0. How far do you go in the 10 sec it takes to pass the truck?
10. A box with a square base with no top has a surface area of 108 square feet. Find the dimensions that will maximize the volume.
11. A park area of 5000 square meters is to be built in the shape of a rectangle along a river. Fencing will be on three sides. What is the minimum length of fencing for the desired area?
12. Find the minimum cost to construct a cylindrical container if material for the top and bottom costs 4 cents per square inch and material for the sides costs 3 cents per square inch. The container is to have volume 100 cubic inches.