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JEE Main20249 Apr 2024Evening ShiftMathematicsApplication of DerivativesActual

Let the set of all values of p , for which f(x)= (p^2-6 p+8 ) ( ^2 2 x- ^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 _______

Correct answer

0

Step-by-step solution

aligned & f(x)=- (p^2-6 p+8 ) 4 n+2(2-p) n+7 & f^1(x)=+4 (p^2-6 p+8 ) 4 x+(4-2 p) 0 & 4 x 2 p-4 4(p-4)(p-2) aligned aligned & 4 x 2(p-2) 4(p-4)(p-2) & p 2 & 4 x 1 2(p-4) & | 1 2(p-4) |>1 aligned on solving we get p ( 7 2 , 9 2 ) Hence a = 7 2 , ~b = 9 2 16 ab =252

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