Let , where is a real parameter. (i) Find all critical points of in terms of . (ii)…

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

f_{k}(x)=x^{3}-3(k+1)x^{2}+3kx+2

, where

k

is a real parameter. (i) Find all critical points of

f_{k}(x)

in terms of

k

. (ii) Determine the set of all real values of

k

for which

f_{k}(x)

is non-decreasing on

(-\infty,0]

and strictly decreasing on

[0,\infty)