# Applying Mean Value Theorem

• May 15th 2011, 10:04 PM
RezMan
Applying Mean Value Theorem
Hi guys can help me with this:

Knowing only that f ’(x) > 2 for all x, can we apply the Mean Value Theorem to f? (For example, given that f(0) = 6, can we conclude anything about the value of f(1)? Explain why MVT can or cannot be applied)?

since f' exists for all x then the function exists for all x, and so it is continuous, right? And since there is a f' then the function is differentiable. And so MVT can be applied. As for the 2nd question, what is there to be said about f(1)?
• May 15th 2011, 10:48 PM
FernandoRevilla
Quote:

Originally Posted by RezMan
And so MVT can be applied.

Right.

Quote:

As for the 2nd question, what is there to be said about f(1)?
Applying the MVT we obtain $f(1)=6+f'(\xi)\quad (0<\xi <1)$ .
• May 16th 2011, 01:56 AM
RezMan
could you explain what that sign is please?
• May 16th 2011, 02:10 AM
FernandoRevilla
Quote:

Originally Posted by RezMan
could you explain what that sign is please?

According to the Mean Value Theorem, there exists $\xi \in (0,1)$ such that

$f'(\xi)=\dfrac {f(1)-f(0)}{1-0}=f(1)-6$