Theorem 6 Let f be a differentiable function on a closed interval I and let c be any
interior point of I Then
(i) f ′(c) = 0 if  f attains its absolute maximum value at c (ii) f ′(c) = 0 if  f attains its absolute minimum value at c In view of the above results, we have the following working rule for finding absolute
maximum and/or absolute minimum values of a function in a given closed interval
[a, b]