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Rationalised 2023-24
 MATHEMATICS
166
Fig 6 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