The closed interval method finds the global maximum and global minimum of a continuous function on a closed interval . The extreme value theorem guarantees that both values are attained.

Evaluate at the endpoints and and at every interior critical point, where or the derivative does not exist. An interior extremum must be a critical point. The largest and smallest of the resulting values are therefore the global maximum and global minimum.

For example, on has a single interior critical point at . The values at 0, 1, and 2 are 0, , and 2, so the global minimum is at and the global maximum is 2 at .

See also

Critical Point, Extreme Value Theorem

Explore with Wolfram|Alpha

References

Strang, G. and Herman, E. J. "Maxima and Minima." §4.3 in Calculus, Vol. 1. Houston, TX: OpenStax, 2016. https://openstax.org/books/calculus-volume-1/pages/4-3-maxima-and-minima.

Cite this as:

Weisstein, Eric W. "Closed Interval Method." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ClosedIntervalMethod.html

Subject classifications