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Critical Points, Local Max/Min

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Presentation on theme: "Critical Points, Local Max/Min"— Presentation transcript:

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….

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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).

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12 Questions c) d) e)

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


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