Question
Find all the points of local maxima and local minima of the function f given by f (x) = 2x3 – 6x2 + 6x + 5 .
Solution
f (x) = 2 x3 – 6 x2 + 6 x + 5
∴ f ' (x) = 6 x2 – 12 x + 6 = 6 (x2 – 2 x + 1)
∴ f ' (x) = 6 ( x – 1)2
Now f ' (x) = 0 ⇒ 6 (x – 1)2 = 0 ⇒ r = 1
When x < 1 slightly, f ' (x) = 6 (1) = + ve
When x > 1 slightly, f ' (x) = 6 (+) = ve
∴ f ' (x) does not change sign as x passes through I
∴ x = 1 is a point of inflexion.
