AM-2089

Differentiating standard functions

A Math · Secondary 4 · Hard · Differentiating standard functions

The curve

y = x + 3\cos\left(\dfrac{x}{2}\right)

is defined for

0 \le x \le \pi

. Find the

x

-coordinate of the stationary point of the curve.

$x = 2\sin^{-1}\left(\dfrac{2}{3}\right)$
$x = \sin^{-1}\left(\dfrac{2}{3}\right)$
$x = 2\cos^{-1}\left(\dfrac{2}{3}\right)$
$x = \pi - 2\sin^{-1}\left(\dfrac{2}{3}\right)$

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