The fuction $f (x) = sin x {cos}^{2} x$ has extremum at

x = π / 2

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x = {cos}^{- 1} (1 / \sqrt{3})

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x = {cos}^{- 1} (\sqrt{2 / 3})

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x = {cos}^{- 1} (- \sqrt{2 / 3})

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Solution

The correct options are
A $x = π / 2$
C $x = {cos}^{- 1} (\sqrt{2 / 3})$
D $x = {cos}^{- 1} (- \sqrt{2 / 3})$
$f (x) = sin x {cos}^{2} x$
$f^{'} (x) = {cos}^{2} x cos x - 2 cos x {sin}^{2} x = cos x (3 {cos}^{2} x - 2)$
For extremum value of $f (x)$
$f^{'} (x) = 0 = cos x (3 {cos}^{2} x - 2)$
$cos x = 0 o r cos x = \pm \sqrt{2 / 3}$
$\Rightarrow x = π / 2, {cos}^{- 1} (\sqrt{2 / 3}), {cos}^{- 1} (- \sqrt{2 / 3})$

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