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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.

What is the deepest amount of fill dirt needed?

When is the highway at its lowest point?

Lesson 3.1Extrema on an Interval

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)

Derivative at Extrema

Find the derivative at the given extreme values.

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

Example

Find the extrema of on [-1, 3]

Example

Problem Set 3.1