3Section 3.1 – Extrema on an IntervalIn this lesson you will learn how to use a derivative to locate the minimum and maximum values of a function on a closed interval.Definition of ExtremaLet fbe defined on an interval Icontaining c.f(c)is the ________________________ of fon Iif f(c)≤f(x)for all xin I.f(c)is the ________________________ of fon Iif f(c)≥f(x)for all xin I.The minimum and maximum of a function on an interval are the extreme values, or extrema, of the function on the interval. The minimum and maximum of the function on an interval are also called the absolute minimumand absolute maximumon the interval. “Global” is sometimes used for “absolute.”The Extreme Value TheoremIf fis continuous on a closed interval [a, b], then fhas both a minimum and a maximum on the interval.Definition of Relative (local) Extrema1. If there is an open interval containing con which f(c)is a maximum, then f(c)is called a _______________________________________of f2. If there is an open interval containing con which f(c)is a minimum, then f(c)is called a ________________________________________of f..