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Modeling Highway Height with Extrema Equations

Learn how to apply extrema concepts to model the highway's height using fill dirt. Find deepest fill amount needed and identify when the highway is at its lowest point. Lesson focusing on extrema on an interval and extrema of a function. Understand critical numbers for determining min/max values. Explore examples to master the concepts.

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Modeling Highway Height with Extrema Equations

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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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