1. ## Mean Value Theorem

Verify that the function satisfies the hypotheses (or conditions) of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusions of the Mean Value Theorem.
$\displaystyle f(x) = 1/x, [1, 3]$

Thank you in advance if anyone can help

2. Originally Posted by ilovemymath
Verify that the function satisfies the hypotheses (or conditions) of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusions of the Mean Value Theorem.
$\displaystyle f(x) = 1/x, [1, 3]$

Thank you in advance if anyone can help
what is the hypothesis of the MVT? once you determine if the function satisfies the hypothesis over the given interval ...

$\displaystyle f'(c) = \dfrac{f(b) - f(a)}{b-a}$

3. The hypotheses of Mean Value Theorem ensures that
(i) The function 'f' is continuous in the closed interval[1,3] and
(ii)The function 'f' is differentiable in the open interval(1,3).

Now what can you say about the differentiability and continuity of the function $\displaystyle f(x)=\frac{1}{x}$ for the given intervals?