If I know a function f(x) I know we can obtain the critical points with the first derivative test; furthermore, we can identify if this points correspond to a maximum or a minimum with the second derivative test.
What happens when I want to get the maximum of a function which I dont't know but I have the first differential df of it?
I have the intuition that I can obtain the critical point simply by equating df = 0, and the max or min by checking the sign of the second differential of f.
Is this true? and if so, why?
Many thanks!
