I must say the veracity of the following statement : If differentiable such that and , then is an increasing function.

My attempt : I don't know how to start. By intuition it's false, so that the exercise show me a difference between one variable functions and several variables functions. I've not found any counter example yet. So it might be true, but I don't know how to prove it.

Any tip will be appreciated. (Not a full answer please)