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Applications of Differentiation Calculus Chapter 3.

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Presentation on theme: "Applications of Differentiation Calculus Chapter 3."— Presentation transcript:

1 Applications of Differentiation Calculus Chapter 3

2 Extrema on an Interval Calculus 3.1

3 3 Extrema Extreme values Minimum (plural minima) Maximum (plural maxima) Can be absolute (on a closed interval) or relative (on an open interval)

4 Calculus 3.14 Critical numbers Where the derivative is zero Or undefined Relative extrema occur only at critical numbers

5 Calculus 3.15 Finding extrema on a closed interval 1.Find the critical numbers 2.Evaluate the function at the critical numbers 3.Evaluate the function at the endpoints of the interval 4.The least of these values is the minimum. The greatest is the maximum

6 Calculus 3.16 Examples Find the absolute extrema of the functions on the given intervals

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