Thinking about slopes on Mungrisdale Common

 We climbed Mungrisdale Common by the Bob Graham route. The slope starts very steep by starts to level off much higher up as you can see.

We would normally call that a convex slope. I was modelling it in my head on the way up as the graph for the square root of positive numbers. f(x) = x^1/2 for x>0. I was differentiating it in the my head. First derivative gives the gradient f '(x) = 1/2x^-1/2 which gives a bigger number for smaller x. Second derivative tells us about the way the gradient changes f ''(x) = -1/4x^-3/2. This will always be negative showing that the gradient is levelling off. However it seems that mathematicians call it a concave function https://en.wikipedia.org/wiki/Concave_function