JEE Mains · Maths · STD 12 - 6. Application of derivatives
The sum of absolute maximum and absolute minimum values of the function \(f(x)=\left|2 x^{2}+3 x-2\right|+\sin x \cos x\) in the interval \([0,1]\) is
- A \(3+\frac{\sin (1) \cos ^{2}(1 / 2)}{2}\)
- B \(3+\frac{1}{2}(1+2 \cos (1)) \sin (1)\)
- C \(5+\frac{1}{2}(\sin (1)+\sin (2))\)
- D \(2+\sin \left(\frac{1}{2}\right) \cos \left(\frac{1}{2}\right)\)
Answer & Solution
Correct Answer
(B) \(3+\frac{1}{2}(1+2 \cos (1)) \sin (1)\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left|2 x^{2}+3 x-2\right|+\sin x \cos x\) \(f(x)=|(2 x-1)(x+2)|+\sin x \cos x\) \(f^{\prime}(x)=\left\{\begin{array}{cl}4 x+3+\frac{\cos 2 x}{4}, & \frac{1}{2} < x < 1 \\ -(4 x+3)+\frac{\cos 2 x}{4}, & 0 \leq x < \frac{1}{2}\end{array}\right.\) For…
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