JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10\). The number of points of local maxima of \(f\) in interval \((0,2 \pi)\) is:
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}(\mathrm{x})=4 \cos ^3(\mathrm{x})+3 \sqrt{3} \cos ^2(\mathrm{x})-10 ; \mathrm{x} \in(0,2 \pi) \) \(\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=12 \cos ^2 \mathrm{x}[-\sin (\mathrm{x})]+3 \sqrt{3}(2 \cos (\mathrm{x}))[-\sin (\mathrm{x})] \)…
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