Math
Extreme values.
Definition
Extreme values are the maximum and minimum values of a function on a given interval. The Extreme Value Theorem states that a continuous function on a closed interval [a, b] must attain both an absolute maximum and an absolute minimum.
How it works · 4 phases
Step by step.
- Find the derivative and set it equal to zero to find critical points
- Evaluate the function at each critical point within the interval
- Evaluate the function at the endpoints a and b
- The largest value is the absolute maximum; the smallest is the absolute minimum
Examples
Real-world.
- 1 Finding the highest and lowest points on a roller coaster modeled by a function
- 2 Determining the maximum profit given a revenue function on a fixed domain
- 3 f(x) = x² on [-2, 3] has a minimum of 0 at x = 0 and a maximum of 9 at x = 3