Find the local extremum values of the following functions:
f(x) = (x – 1) (x – 2)2
f(x) = (x – 1)(x – 2)2
f’(x) = (x – 2)2 + 2(x – 1)(x – 2)
= (x – 2)(x – 2 + 2x – 2)
= (x – 2)(3x – 4)
f’’(x) = (3x – 4) + 3(x – 2)
For maxima and minima,
f'(x) = 0
(x – 2)(3x – 4) = 0
x = 2, 4/3
Now
f’’(2) > 0
x = 2 is point of local minima
f’’(4/3) = – 2 < 0
x = 4/3 is point of local maxima
hence
local max value = f(4/3) = 4/27
local min value = f(2) = 0