No. You can take for example the curve y = -x^2

At -1, the gradient (ie f'(-1)) is 2 and at 0, the gradient is 0.

This means that f'(-1) > f'(0)

But you know that f(-1) = -1 and f(0) = 0

So, f(-1) \cancel{>} f(0)

well then, how shall we determine whether the statement is true or not in page 3, q4, a), 1. in the following link:
http://elearning.ppu.edu/mod/resource/view.php?id=14978

I'm afraid you'll have to post the question. I have to register to be able to see the question and that's not something I like to do on any site I don't know much about.