1. Entry Task 11/17 WK11 -Please have out a pencil, your notebook and your HW from last night 424/6,9,10 & Related Rates WS -Tonight’s HW is: pg. 431/1-4 Compare with your neighbor the HW from last night and present problems 1 & 2

2. HW

4. Notes/Partner Work Optimization Head your notes with, “I can create a big idea equation to model the situation, then determine and classify stationary points or endpoints as local max’s or mins to answer the question in a mathematical sentence.“

5. Notes/Partner Work Optimization Is used to find a minimum or maximum value of a process/function. The solutions are optimal solutions, hence optimization. Can determine a max or min with a calculator and graph, the vertex of a parabola, but also using CALCULUS! (f’(x)=0) Warning!?!: A max or min value does not always occur when the derivative is zero, could happen at an endpoint of a restricted domain.

6. Private Think Time Individually brainstorm What are our ways of determining a max or min currently? Optimization

7. Turn and Talk Person who is wearing more warm colors ask first: What ways do you know to calculate max or min? Doesn’t have to be calculus based. Optimization

8. Notes/Partner Work Optimization The steps to solving an Optimization Problem 1. Clear Picture/Diagram 2.A “Big Idea” equation that represents the situation, include any domain restrictions. 3.Determine the stationary points (f’(x)=0) 4.Classify the stationary points using 1 st Derivative sign chart, 2 nd derivative test or using a graph. (compare to endpoints) 5.Answer the question in a mathematical sentence. Example:

9. Partner/Group Work

11. Reflection/Private Think Time Think about this…. Below is a picture of a helix with its parametric equation, How does that equation make this helix?