Question
Find the points at which the function f given by f (x) = (x – 2)4 (x + 1 )3 has
(i) local maxima (ii) local minima (iii) point of inflexion .
Solution
Here, 
When x < 2 slightly, 
When x > 2 slightly, 
When x < -1 slightly f ' (x) = (-) (+) (-) = +ve
When x > -1 slightly, f ' (x) = (-) (+) (-) = +ve
at x = -1, f ' (x) does not change sign
x = -1 is a point of inflexion.
