Suppose that {{MATH_477}} is continuous on an open interval, and that {{MATH_478}} has a critical point at {{MATH_479}}, for some value {{MATH_480}} in that interval. {{CMD_481}} {{CMD_482}} If {{MATH_483}} to the left of {{MATH_484}} and {{MATH_485}} to the right of {{MATH_486}}, then the function {{MATH_487}} has a local maximum at {{MATH_488}}. {{CMD_489}} If {{MATH_490}} to the left of {{MATH_491}} and {{MATH_492}} to the right of {{MATH_493}}, then the function {{MATH_494}} has a local minimum at {{MATH_495}}. {{CMD_496}} If {{MATH_497}} has the same sign to the left and right of {{MATH_498}}, then the function {{MATH_499}} has no local extremum at {{MATH_500}}. {{CMD_501}} {{CMD_502}}