Application Of Derivatives

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