Write sufficient conditions for a point x=c to be a point of local maximum.

We know that at the extreme points of a function f(x), the first order derivative of the function is equal to zero, i.e.
f '(x) = 0 at x = c
⇒">⇒⇒f '(c) = 0

Also, at the point of local maximum, the second order derivative of the function at the given point must be less than zero, i.e.
f ''(c) < 0