15
Example 18 Find all the points of local maxima and local minima of the function f
given by
f (x) = 2x3 – 6x2 + 6x +5 Solution We have
f (x) = 2x3 – 6x2 + 6x + 5
or
f ′(x) = 6x2 – 12x + 6 = 6(x – 1)2
or
f ′(x) = 0    at   x = 1
Thus, x = 1 is the only critical point of  f We shall now examine this point for local
maxima and/or local minima of f Observe that f ′(x) ≥ 0, for all x ∈ R and in particular
f ′(x) > 0, for values close to 1 and to the left and to the right of 1