Mathematics · Application of Derivatives

JEE Main 2024 — 8 April, Shift 1 — Question 7

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:

Answer: B

$f(x)=4 \cos ^{3}(x)+3 \sqrt{3} \cos ^{2}(x)-10 ; x \in(0,2 \pi)$

$\Rightarrow f^{\prime}(\mathrm{x})=12 \cos ^{2} \mathrm{x}[-\sin (\mathrm{x})]+3 \sqrt{3}(2 \cos (\mathrm{x}))[-\sin (\mathrm{x})]$

$\Rightarrow \mathrm{f}^{\prime}(\mathrm{x})=-6 \sin (\mathrm{x}) \cos (\mathrm{x})[2 \cos (\mathrm{x})+\sqrt{3}]$

local maximum at $x=\frac{5 \pi}{6}, \frac{7 \pi}{6}$

Answer key and solution verified before publishing.

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