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3.1 Extrema on an Interval

3.1 Extrema on an Interval. Questions that will be answered in Chapter 3:. Does f have a maximum or a minimum value? Where is the function increasing or decreasing? Applications? Derivative will help us! . 3.1 Extrema on an Interval. 3.1 Extrema on an Interval .

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3.1 Extrema on an Interval

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  1. 3.1 Extrema on an Interval

  2. Questions that will be answered in Chapter 3: • Does f have a maximum or a minimum value? • Where is the function increasing or decreasing? • Applications? • Derivative will help us!

  3. 3.1 Extrema on an Interval

  4. 3.1 Extrema on an Interval • Does this make sense? • Visualize a picture in your head

  5. 3.1 Relative Extrema and Critical Number. • Notice the endpoints or breaks in the graph cannot be relative extrema since it requires open intervals • Only hills and valleys

  6. Example 1: The Value of the Derivative at Relative Extrema

  7. 3.1 Critical Number Be careful don’t get confused with the converse

  8. 3.1 Finding Extrema on a Closed Interval • Step 1 and 2 will find the highest and lowest relative extreme • Step 3 will see if the other extremas are higher than these

  9. Example 2: Finding Extrema on a Closed Interval

  10. Your turn

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