Mathematics - Application of Derivative Question with Solution | TestHub

If the function$f$given by$f\left(x\right)=x^3-3\left(a-2\right)x^2+3ax+7$, for some$a\in R$is increasing in$\left(0, 1\right]$and decreasing in$\left[1, 5\right)$, then a root of the equation,$\frac{f\left(x\right)-14}{{\left(x-1\right)}^2}=0, \left(x\ne 1\right)$is :