The mean value theorem
the mean value theorem (MVT) is an extremely important theorem in calculus. it states that:
If f is continuous on the compact a≤x≤b and differentiable on a< x
Use the mean Value theorem to prove that |cosb-cosa|≤|b-a|, for any real values a and b.
Let f(x) = cosx. f satisfies the demands of the mean Value theorem because it is continuous on in any close interval and differentiable on any open interval on R, the set of real numbers.
f'(x) = – sinx
so, f(b) – f(a) = (b-a)f'(c), where a
About The Author
|Maths Expert And SAT Instructor|
|Experience High school/college teacher with many years of experience.I have a wide range of teaching and preparing students in test preps, i have been involved in many symposiums in mathematics and I also write and contribute in writing maths textbooks. I am a curriculum developer and also a program...|