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Application of Derivatives question

2023 · 12 Apr · Shift 1 · Q32

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JEE Main
Mathematics
Application of Derivatives
2023 · 12 Apr · Shift 1 · Q32

Application of Derivatives question

2023 · 12 Apr · Shift 1 · Q32

JEE MainMathematicsApplication of DerivativesMCQ+4 / −1

If the local maximum value of the function

f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0, \frac{\pi}{2}\right)

, is

\frac{k}{e}

, then

\left(\frac{k}{e}\right)^{8}+\frac{k^{8}}{e^{5}}+k^{8}

is equal to

A
$e^{3}+e^{6}+e^{10}$
B
$e^{3}+e^{5}+e^{11}$
C
$e^{3}+e^{6}+e^{11}$
D
$e^{5}+e^{6}+e^{11}$

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