1. Optimization and Related Rates
By: Andrew, Chirag, and David

2. What is optimization? What are related rates?

3. Card 26: Steps for Solving an Optimization Problem
Draw a picture of the physical situation (if applicable)
Write an equation that relates the quantity you want to optimize in terms of the relevant variables
If necessary, use other given information to rewrite your equation in terms of a single variable.
Take the derivative of your equation with respect to your single variable and find the critical points
Determine the maxima and minima as necessary (remember to check endpoints!!)
Justify your max or min with the first or second derivative test

4. Optimization Free Response Practice
Optimization FRQ #16

5. Card 27: Common Formulas to Know for Related Rates
Triangle:
Area= (½)bh
Pythagorean Theorem:
a2 + b2 = c2
Circle:
Area = πr2
Circumference = 2πr
Cone:
Volume = (⅓)πr2 h
Sphere:
Volume = (4/3)πr3
Surface Area = 4πr2
Cylinder:
Volume = πr2h
Surface Area = 2πrh + 2πr2
HINT: Take the derivative of the Volume to find the Surface Area of a 3D shape!

6. Related Rates Multiple Choice Practice

7. Card 28: Steps for Solving a Related Rates Problem
Draw a picture of the situation described in the problem (if applicable)
List all given information and the quantities to be determined
Label each quantity that varies with time with an appropriate variable
Label each quantity that does not vary with its constant value
Relate the variables in an equation and make appropriate substitutions
Differentiate both sides of the equation with respect to time
Substitute known quantities into the result and solve for the unknown quantity (DON’T FORGET UNITS)

8. Related Rates Free Response Practice
Related Rates FRQ #11

9. Optimization: 1, 4-15, 17 Related Rates: 3, 5-10, 12-13, 15
Tonight’s Homework
Optimization:
1, 4-15, 17
Related Rates:
3, 5-10, 12-13, 15