## Calculus Tutorial

*The mean value theorem*

#### Intro

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 **
**

#### Sample Problem

Use the mean Value theorem to prove that |cosb-cosa|≤|b-a|, for any real values a and b.

#### Solution

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

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