Derivatives will be more helpful when considering not global extrema, but their local counterparts. A {{CMD_56}}local extremum{{CMD_57}} of a function {{MATH_58}} is a point {{MATH_59}} on the graph of {{MATH_60}} where the {{MATH_61}}-coordinate is larger (or smaller) than all other {{MATH_62}}-coordinates of points on the graph whose {{MATH_63}}-coordinates are ``close to'' {{MATH_64}}.