AP EAMCET · Maths · Application of Derivatives
If \(f(x)=\sqrt{3} \sin x-\cos x-2 a x+b\) decreases for all values of \(x\), then
- A \(a \geq 1\)
- B \(a=1\)
- C \(a \leq 1\)
- D \(a < 1\)
Answer & Solution
Correct Answer
(A) \(a \geq 1\)
Step-by-step Solution
Detailed explanation
\(f(x)=\sqrt{3} \sin x-\cos x-2 a x+b\) \(\Rightarrow f^{\prime}(x)=\sqrt{3} \cos x+\sin x-2 a\) \(\begin{aligned} & =2\left(\frac{\sqrt{3}}{2} \cos x+\frac{1}{2} \sin x\right)-2 a \\ & =2 \sin \left(x+\frac{\pi}{3}\right)-2 a\end{aligned}\) When, \(f(x)\) decreases. Then,…
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