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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. Extrema of a Function

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Write an equation to model the height of the highway.

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  1. 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?

  2. Lesson 3.1Extrema on an Interval

  3. 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)

  4. Derivative at Extrema Find the derivative at the given extreme values.

  5. 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

  6. Example Find the extrema of on [-1, 3]

  7. Example Problem Set 3.1

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