MATH 140 Lecture Notes - Lecture 20: Mean Value Theorem, If And Only If

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: Gulick

Document Summary

Math140 lecture 20 finding relative extrema. Mean value theorem: let f be continuous on [a, b] and let f " exist on (a, b). Then there is a c in (a, b) with (c) f f(b) f(a) Antiderivatives: antiderivatives of f have the form f (x); f "(x) = f (x) x. = 4 x3: f increases on an interval i if f " > 0 for all x in i , f decreases on an interval i if f " < 0 for all x in i . = x: note 2: g can have relative extreme values but no extreme values. Let f " exist on an open interval i about c . Assume that f "(c) = 0 and that f " changes sign at c . x x x x. = x3 3 2 9 1 (x.