Let the set of all values of p, for which f(x)=(p^2-6 p+8)( sin^2 2 x- cos^2 2 x)+2(2-p) x+7 does not have any critical point, be the interval (a,…

Let the set of all values of $\displaystyle p$, for which $\displaystyle f(x)=\left(p^2-6 p+8\right)\left(\sin ^2 2 x-\cos ^2 2 x\right)+2(2-p) x+7$ does not have any critical point, be the interval $\displaystyle (a, b)$. Then $\displaystyle 16 a b$ is equal to $\displaystyle \_\_\_\_$.