1. 6.5: RELATED RATES OBJECTIVE: TO USE IMPLICIT DIFFERENTIATION TO RELATE THE RATES IN WHICH 2 THINGS ARE CHANGING, BOTH WITH RESPECT TO TIME.

2. RELATED RATES GUIDELINES 1. Make a sketch. Label all sides in terms of variables, even if you are given the actual values of the sides. 2. Make a list of variables. Separate them into variables that are constant (never change) and variables that are changing (variables that are a given value only at a certain point in time). Rates (recognized by “increasing”, “decreasing”, etc.) are derivatives with respect to time. They can go into either category. Be aware if the rate is positive or negative (increasing vs. decreasing over time). 3. Find an equation which ties your variables together. If it is an area problem, you need an area equation. If it is a right triangle, the Pythagorean formula may work, etc. 4. Plug in value for any variable that is constant. NEVER plug in a variable that is changing before you differentiate!!! 5. Use implicit differentiation to differentiate you equation with respect to time, t. 6. Plug in all variables and known rates. Solve for the unknown rate. 7. Label your answers in terms of the correct units ( very important), and be sure you answered the question asked.

3. THINGS TO REMEMBER……  Words such as “rate” and “speed” are code words for derivative, where the underlying variable is time, t.  Be aware of positive vs. negative rates of change. Is “something” increasing or decreasing over time?  If “something” is constant or does not change over time, the rate of change, or derivative, is 0.

4. HANDOUT A # 1

5. HANDOUT A # 2