Hi guys can help me with this:

Knowing only thatf ’(x)> 2 for all x, can we apply the Mean Value Theorem tof? (For example, given thatf(0) = 6, can we conclude anything about the value off(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)?