# Thread: Applying Mean Value Theorem

1. ## 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)?

2. Originally Posted by RezMan
And so MVT can be applied.
Right.

As for the 2nd question, what is there to be said about f(1)?
Applying the MVT we obtain $\displaystyle f(1)=6+f'(\xi)\quad (0<\xi <1)$ .

3. could you explain what that sign is please?

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

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

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