1. Critical Points, Local Max/Min
Mr.S.Paramasamy

2. Learning Goal/ Big idea
Learning Goal: The students will learn to find and categorize critical points, local Max/Min for various functions by finding the first and second derivatives.
Big Idea: Limited information about a mathematical relationship some times, but not always, allows us to predict other information about that relationship.

3. Minds ON
What can you say about the polynomial function
f(x)=-2x3-6x2+12x+16

4. In the last lesson, we mostly considered the max/min on an interval
In the last lesson, we mostly considered the max/min on an interval. Now we consider the max/min over the domain of the function. For example….

8. FDT! FIRST DERIVATIVE TEST!!!
Notice that when the sign of the slope changes we have a max or a min. Which brings us to the
FIRST DERIVATIVE TEST!!!
If the derivative changes sign from positive to negative, then the function has a local max.
If the derivative changes sign from negative to positive, then the function has a local min.

9. ( ) , ¥ 8x + 5 4 y Decreasing Increasing
Example: Use the critical points to find any max or min for the following functions…. 3 24 8 = \ - x
when dx dy ( ) , 8x + 5 4 2 y
Decreasing
Increasing
Therefore there is a min at x=3. Or the point (3,-31).

12. Questions c) d) e)

13. Exit ticket
Write a polynomial which has two local minimum and one absolute maximum at .