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 3.1 Extrema on an Interval. Extrema of a Function

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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

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

Lesson 3.1Extrema on an Interval


Write an equation to model the height of the highway

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)


Write an equation to model the height of the highway

Derivative at Extrema

Find the derivative at the given extreme values.


Write an equation to model the height of the highway

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


Write an equation to model the height of the highway

Example

Find the extrema of on [-1, 3]


Write an equation to model the height of the highway

Example

Problem Set 3.1


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