1. Section 2.6
Related Rates

2. What is a rate? A rate is a change of quantity with respect to time.
Related rates problems show us how some rates are connected through equations.

3. Ex: Spongebob Squareface is growing so his edge is increasing at a rate of 5 cm/second. How fast is the area of his face changing when the edge is 3 cm?

4. Steps for Related Rates: PGWEDA
Picture (draw a picture, include variables) Given (identify given information, what you know) Want (identify what you want to know/find) Equation (find an equation to relate the variables) Derivative (take derivative with respect to time) Answer (plug in values to get answer)

5. Ex: At noon, 2 trains leave Oceanside. Thomas travels north at 65 mph
Ex: At noon, 2 trains leave Oceanside. Thomas travels north at 65 mph. Percy travels east at 70 mph. Find the rate at which the distance between the 2 trains is changing at 2 PM.
Oceanside

6. Ex: A spotlight on the ground shines on a building 12 m away
Ex: A spotlight on the ground shines on a building 12 m away. If a man (who is 2 m tall) walks from the spotlight toward the building at a speed of 1.6 m/sec, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?