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
What is the deepest amount of fill dirt needed?
When is the highway at its lowest point?
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)
Find the derivative at the given extreme values.
► 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
Find the extrema of on [-1, 3]
Problem Set 3.1