f'(x) > 0 means the change in f(x) is always directly related with respect to the change in x.

This suggests that f(x) always increases as x increases.

So f(x) is an increasing function.

Well, we could simply say that the gradients of the curve at any point are always positive, suggesting that the curve is always heading upwards

It depends on the direction you are heading in x.

If x is heading backwards i.e decreasing f(x) will decrease, which means f(x) is heading downwards.


Increasing function means with respect to an increase in x.