Fig 6 14
Example 17 Find all points of local maxima and local minima of the function f
given by
f (x) = x3 – 3x + 3 Solution We have
f (x) = x3 – 3x + 3
or
f ′(x) = 3x2 – 3 = 3(x – 1) (x + 1)
or
f ′(x) = 0 at x = 1 and x = – 1
Thus, x = ± 1 are the only critical points which could possibly be the points of local
maxima and/or local minima of f Let us first examine the point x = 1