Let f  be twice differentiable at c Then
 (i) x = c is a point of local maxima if f ′(c) = 0 and f ″(c) < 0
The values f (c) is local maximum value of  f (ii)
x = c is a point of local minima if f ′(c) = 0 and f ″(c) > 0
In this case, f (c) is local minimum value of  f (iii) The test fails if f ′(c) = 0 and f ″(c) = 0