MATH 111 Lecture Notes - Lecture 18: Maxima And Minima, Mean Value Theorem
18 Jun 2015
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1476- lecture 18 - the mean value theorem and how derivatives affect the shape of a. 3. f is continuous on the closed interval [a,b] f is differentiable on the open interval (a,b) f(a) = f(b) Then, there is a number c in (a,b) such that f ( c) = 0. 2. f is continuous on the closed interval [a,b] f is differentiable on the open interval (a,b) Then, there is a number c in (a,b) such that: Or, there is at least one point where the instantaneous slope is equivalent to the average slope. This theorem can be used to find extreme values of f(x) Theorem: if f (x)= 0 for all x in an interval (a,b), then f (x) is constant on (a,b) Corollary: if f (x)= g (x) for all x in an interval (a,b), then f(x) = g(x) + c [with c as a constant] Estimate the value of f(x) using f (x)
