1. Hold on to your homework

2. Answers to Implicit Differentiation Day 2 Homework2. 1.

3. Answers to Implicit Differentiation Day 2 Homework3. 4.

4. Quiz

5. Related Rates
Day 1

6. Distance from the wall, x
If a ladder is pulled away from a wall at a steady rate, will the top of the ladder slide down the wall at the same rate?
Use a 12-inch ruler as your ladder.
Place the ladder flat against a wall. Move the bottom of the ladder 2 inches away from the wall and measure the height h that the top of the ladder reaches on the wall. Move the bottom of the ladder another 2 inches out, and measure the new height. Record your data in the table. All measurements are in inches.
Distance from the wall, x
Height, h 2 4 6 8 10 12

7. What is true about the rate of change of x with respect to time?
Is the rate of change of the height constant?

8. Since the rate of change of the height varies over time, to find the instantaneous rate of change of height with respect to time, written , find the derivative (with respect to time) of the an equation relating x and h.

9. What will always be true on this diagram
What will always be true on this diagram? What will be changing over time?

10. A 12 ft long ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 2 ft/sec, how fast is the top of the ladder sliding down the wall when the top of the ladder is 8 ft. from the ground?

11. Write the following statements mathematically
John’s height is changing at the rate of 3 in./year
The volume of a cone is decreasing by 2 in3/min.
The radius of a circle in increasing at 4 ft. per hour

12. A rectangle has length l and width w.
Write an equation to represent the rate of change of the perimeter.
What is the rate of change of the perimeter if the length is increasing at 2 inches /min. and the width is decreasing 3 inches/min.?

13. A rectangle has length l and width w.
Write an equation to represent the rate of change of the area.
If the length is decreasing at 2 inches/min. and the width is increasing 1.5 inches/min., What is the rate of change of the area when the length is 10 and the width is 4?

14. Air is being pumped into a spherical balloon at the rate of 4
Air is being pumped into a spherical balloon at the rate of 4.5 cubic inches per minute. Find the rate of change of the radius when the radius is 2 inches.

15. A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a constant rate of 1.2 feet per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

16. All edges of a cube are expanding at the rate of 5 cm/sec.
How fast is the surface area changing when the length of each edge is 12 cm?
How fast in the volume changing when the length of each edge is 12 cm?

17. Darth Vader's spaceship is approaching the origin along the positive y-axis at 50 km/sec. Meanwhile his daughter Ella's spaceship is moving away from the origin along the positive x-axis at 80 km/sec. When Darth is at y = 1200 km and Ella is at x = 500 km, is the distance between them increasing or decreasing? At what rate?