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Write an equation to model the height of the highway.

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Write an equation to model the height of the highway. - PowerPoint PPT Presentation


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Write an equation to model the height of the highway. What is the deepest amount of fill dirt needed? When is the highway at its lowest point?. Lesson 3.1 Extrema on an Interval. Extrema of a Function

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Presentation Transcript
slide1
Write an equation to model the height of the highway.

What is the deepest amount of fill dirt needed?

When is the highway at its lowest point?

slide4
Extrema of a Function

An x value, c, produces a minimum, f(c), if f(c) is the lowest y-value on some interval

Produces a maximum if f(c) is the highest y-value.

Absolute min/max: highest in the interval

Relative min/max: highest in an open region (smaller interval)

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Derivative at Extrema

Find the derivative at the given extreme values.

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Critical Numbers

► A critical number, c, occurs at a relative minimum or maximum

► f’(c) = 0 or f’(c) does not exist.

► Critical numbers and endpointsare only possibilities for extrema

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Example

Find the extrema of on [-1, 3]

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Example

Problem Set 3.1

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