JEE Mains · Maths · STD 12 - 6. Application of derivatives
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 ..........
- A \(180\)
- B \(252\)
- C \(754\)
- D \(254\)
Answer & Solution
Correct Answer
(B) \(252\)
Step-by-step Solution
Detailed explanation
\( f(x)=-\left(p^2-6 p+8\right) \cos 4 n+2(2-p) n+7 \) \( f^1(x)=+4\left(p^2-6 p+8\right) \sin 4 x+(4-2 p) \neq 0 \) \( \sin 4 x \neq \frac{2 p-4}{4(p-4)(p-2)}\) \(\sin 4 x \neq \frac{2(p-2)}{4(p-4)(p-2)} \) \(p \neq 2 \) \(\sin 4 x \neq \frac{1}{2(p-4)}\)…
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