If the function f(x)=x3−3(a−2)x2+3ax+7, for some a∈R is increasi – InterviewSolution

1.	If the function f(x)=x3−3(a−2)x2+3ax+7, for some a∈R is increasing in (0,1] and decreasing in [1,5), then a root of the equation f(x)−14(x−1)2=0 (x≠1) is equal to
Answer» If the function $f (x) = x^{3} - 3 (a - 2) x^{2} + 3 a x + 7,$ for some $a \in R$ is increasing in $(0, 1]$ and decreasing in $[1, 5),$ then a root of the equation $\frac{f (x) - 14}{(x - 1)^{2}} = 0 (x \neq 1)$ is equal to

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