Higher Order Derivative Test

If f is differentiable function on an interval I and if c is a point in that interval such that

(i) f’(c) = f’’(c) = f^n-1 (c) =0
(ii) fⁿ (c) exists and is non zero.

If n is even and ) fⁿ (c) l.t. 0 then x =c is a point of local maximum.
If n is even and ) fⁿ (c) g.t. 0 then x =c is a point of local minimum.

In n is odd then x = c is neither a point of maximum or minimum