3.1 Extrema on an Interval
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3.1 EXTREMA ON AN INTERVAL
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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!
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3.1 EXTREMA ON AN INTERVAL
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3.1 EXTREMA ON AN INTERVAL
•Does this make sense?•Visualize a picture in your head
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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
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EXAMPLE 1: THE VALUE OF THE DERIVATIVE AT RELATIVE EXTREMA
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3.1 CRITICAL NUMBER
Be careful don’t get confused with the converse
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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
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EXAMPLE 2: FINDING EXTREMA ON A CLOSED INTERVAL
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YOUR TURN