Let the set of all values of p, for which f(x)=(p²-6 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, b). Then 16 a b is equal to _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 9 Apr, Evening shift · Q27

JEE Main 20249 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let the set of all values of

p

, for which

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

(a, b)

. Then

16 a b

is equal to _________.

Your answerType your answer. Integers and decimals are accepted.