Question

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

Answer 1

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`