1. Teresita S. Arlante Naga City Science High School

2.  Another synonym for the word derivative is rate or rate of change.  When you hear the word rate you should identify d/dt, since rate always corresponds to the derivative with respect to time.

4. 1) Draw the picture (if applicable). 2) Identify what derivatives are known. 3) Identify what derivative is asked for.

5. 4 ) Find an equation that relates only the variables for which the derivative are known and the variable for which the derivative is asked for.

6. 5) Implicitly take the derivative with respect to t (apply d/dt to both sides of the equation) 6) Plug in all known constants 7) Answer the question.

7. The radius of a spherical balloon is increasing at a rate of 5 inches per minute. Find the rate of change of the volume when r = 3 inches.

8. The radius of a spherical balloon is increasing at a rate of 5 inches per minute. Find the rate of change of the volume when r = 3 inches.

9. The radius of a spherical balloon is increasing at a rate of 5 inches per minute. Find the rate of change of the volume when r = 3 inches.

15. A cone with circular base is being filled with water. Find a formula which find the rate with which the water is pumped.

17. Suppose that an inflating balloon is spherical in shape, and its radius is changing at the rate of 3 cm/s. At what rate is the volume changing when the radius is 10 cm?

18. A 14-foot ladder rests vertically against the side of a house. An absent-minded worker begins dragging the bottom of the ladder away from the house at a rate of 2.5 feet per second, not noticing that another worker is standing at the top of the ladder. After a delayed reaction of 2 seconds, the worker on the ladder yells out. How fast is he moving down the wall when he yells?

19. A ladder 10 ft long is resting against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1 ft/s, how fast is the top of the ladder moving down when the bottom of the ladder is 8 ft from the wall?

20. A circle is decreasing in size at the rate of 5 square inches per minute. At what rate is the radius decreasing when the radius is 4?

21. As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6 in/min, find the rate at which the sand is leaking out when the altitude is 10 in.

22. Air is being pumped into a spherical balloon such that its radius increases at the rate of 0.75 in/min. Find the rate of change of its volume when the radius is 5 inches.

23. A car is traveling north toward an intersection at a rate of 60 mph while a truck is traveling east away from the intersection at a rate of 50 mph. Find the rate of change of the distance between the car and truck when the car is 3 miles south of the intersection and the truck is 4 miles east of the intersection.

24. A spherical hot air balloon is being filled with air. The volume is changing at a rate of 2 cubic feet per minute. How is the radius changing with respect to time when the radius is equal to 2 feet?

25. An airplane is attempting to drop a box onto a house. The house is 300 ft away in horizontal distance and 400 ft in vertical distance. The rate of change of the horizontal distance with respect to time is the same as the rate of change of the vertical distance with respect to time. How is the distance between the box and the house changing with respect to time at the moment? The rate of change in the horizontal direction with respect to time is -50 ft/s.

26. Sand falls onto a cone shaped pile at a rate of 10 cubic feet per minute. The radius of the pile's base is always 1/2 of its altitude. When the pile is 5 ft deep, how fast is the altitude of the pile increasing?

27. A 10 ft long ladder is leaning against a vertical wall. The foot of the ladder is being pulled away from the wall at a constant rate of 2 ft/sec. When the ladder is exactly 8 ft from the wall, how fast is the top of the ladder sliding down the wall?

28. A baseball diamond is 90 square feet, and the pitcher's mound is at the center of the square. If a pitcher throws a baseball at 100 mi/hr, how fast is the distance between the ball and first base changing as the ball crosses home plate?

29. Thank You