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

Answer 1

Now, as the value of x varies through −1, f ' (x) does not changes its sign.
Thus, x = −1 is the point of inflexion.