Let f(x) `=x^(3) =x^(2) -x-4`
(i) find the possible points of maxima `//`minima of f(x) ` x in R`
(ii) Find the number of critical points of f(x) ` x in [1,3]`
(iii) Discuss absolute (global) maxima `//` minima value of f(x) for `x in [-2,2]`
(iv) Prove that for `x in (1,3)` the function does not has a Global maximum.

Answer

(i) x=-1 , (1)/(3)" "zero`
(iii) `f(-2) =-6` is global maximum f(2) =6 is global maximum.