Download presentation
Presentation is loading. Please wait.
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 .
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.