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Previous Year Question (PYQs)



The function $f(x)=2\sin x+\sin 2x,\ x\in[0,2\pi]$ has absolute maximum and minimum at





Solution

$f'(x)=2\cos x+2\cos 2x$ 
$=2(2\cos^2x+\cos x-1)$ 
Critical points: 
$\cos x=\frac{1}{2},-1$ 
$x=\frac{\pi}{3},\pi,\frac{5\pi}{3}$ 

Check values → max at $\frac{\pi}{3}$, min at $\frac{5\pi}{3}$


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