At x=5 6 , f(x)=2 3 x+3 3 x is - Vidyadip

MCQ

At $x=\frac{5 \pi}{6}, f(x)=2 \sin 3 x+3 \cos 3 x$ is

A
maximum
B
minimum
C
zero
✓
neither maximum nor minimum

✓

Answer

Correct option: D.

neither maximum nor minimum

$f(x)=2 \sin 3 x+3 \cos 3 x$
$f^{\prime}(x)=2 \cos 3 x \cdot 3+3(-\sin 3 x) \cdot 3$
$f^{\prime}(x)=6 \cos 3 x-9 \sin 3 x$
For maxima or minima, $f^{\prime}(x)=0$
$\Rightarrow 6 \cos 3 x-9 \sin 3 x=0 \Rightarrow \tan 3 x=\frac{6}{9}=\frac{2}{3}$
$\therefore f(x)$ is neither max. nor min. at $x=\frac{5 \pi}{6}$

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