Let $f\left(x\right)=2{\cos }^{-1}x+4{\cot }^{-1}x-3x^2-2x+10,x\in [-1,1]$. If [a, b] is the range of the function then 4a- b is equal to:

$\begin{array}{l}{f}^{\mathrm{\prime }}\left(x\right)=\frac{-2}{\sqrt{1-x^2}}-\frac{4}{1+x^2}-6x-2\\ =-2\left[\frac{1}{\sqrt{1-x^2}}+\frac{2}{1+x^2}+3x+1\right]\\ f^{\mathrm{\prime }}\left(x\right)<0\Rightarrow f\left(x\right)\text{ is a decreasing. function }\\ f\left(1\right)=\pi +5\\ f(-1)=5\pi +9\\ \text{ Range }:[a,b]\equiv [\pi +5,5\pi +9]\\ \text{ a }=\pi +5,b=5\pi +9\Rightarrow 4a-b=11-\pi \end{array}$