CAS MA 123 Lecture Notes - Lecture 26: Mean Value Theorem

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 123
• Professor: John Bergdall

Document Summary

Ma123 lecture 26 the mean value theorem. There is a point c in (a,b) where f"(c) = 0. It would be enough to construct (or to show exists) a local extreme value in (a,b) F(x) is continuous on [a,b] and is differentiable on (a,b) then there exists at least one point x=c f (b) f (a) b a. If you drive for one hour and go 60 miles in that hour then at some point you were traveling at. F(x) = x3 x average rate of change [0,2] is 6/2=3. Get f(c) = 3 when 3c2 1 = 3 >>> c = 4. Recall we might think of d/dx as an operation that takes one function and returns a new function. Apply 2 to deduce 1 using g(x) = 0. Also can use 1 to deduce 2 given f(x) and g(x), apply 1 to h(x) = g(x) f(x) (h"(x) = g"(x) f"(x) = 0)