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 , b ) . Then 16 ab is equal t

Question

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 , b ) . Then 16 ab is equal to _______

TestHub · Accepted Answer

​ f ( x ) = − ( p 2 − 6 p + 8 ) cos 4 n + 2 ( 2 − p ) n + 7 f 1 ( x ) = + 4 ( p 2 − 6 p + 8 ) sin 4 x + ( 4 − 2 p )  = 0 sin 4 x  = 4 ( p − 4 ) ( p − 2 ) 2 p − 4 ​ ​ ​ sin 4 x  = 4 ( p − 4 ) ( p − 2 ) 2 ( p − 2 ) ​ p  = 2 sin 4 x  = 2 ( p − 4 ) 1 ​ ⇒ ​ 2 ( p − 4 ) 1 ​ ​ > 1 ​ on solving we get ∴ p ∈ ( 2 7 ​ , 2 9 ​ ) Hence a = 2 7 ​ , b = 2 9 ​ ∴ 16 ab = 252

Mathematics - Application of Derivative Question with Solution | TestHub

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