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.
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.

Given: ……….(i)

Now 

= 0

  or  or 

  or  or 

Now, for values of  close to  and to the left of . Also for values of  close to  and to the right of .

Therefore,  is the point of local maxima.

Now, for values of  close to 2 and to the left of . Also for values of  close to 2 and to the right of .

Therefore,  is the point of local minima.

Now as the values of  varies through  does not change its sign. Therefore,  is the point of inflexion.