COMEDK · Maths · 27. Application of Derivatives
The maximum of the function \(3 \cos x-4 \sin x\) is
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
We know that, \[ \begin{aligned} & a \sin x+b \cos x \leq \sqrt{a^{2}+b^{2}} \\ \therefore & 3 \cos x-4 \sin x \leq \sqrt{(-4)^{2}+(3)^{2}}=\sqrt{16+9}=5 \\ \therefore & \text { Maximum value is } 5 . \end{aligned} \]
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