Theorem 2 Let  f  be a function defined on an open interval I Suppose c ∈ I be  any
point If f  has a local maxima or a local minima at x = c, then either f ′(c) = 0 or f  is not
differentiable at c Remark The converse of above theorem need not
be true, that is, a point at which the derivative vanishes
need not be a point of local maxima or local minima