Intuition for the second spatial derivative

[joo]

Hello !

Could you please give me some kind of intuition of the physical meaning of the second spatial derivative ?

I see it all the time, but I have difficulty comprehending it to the same level I have done with the second time derivative.

Thanks !

 

[Simon Bridge]

y=f(x)

y' is how the slope of f(x) varies with x
y'' is how the curvature of f(x) varies with x

i.e. you have a landscape with a hill in it, then y'(x) is how steep the hill is, and y''(x) is how curvey it is.