Question

The number of values of $x$, where the function $f\left(x\right)=\cos x+\cos \left(\sqrt{2}x\right)$ attains its maximum is

• A. $0$
• B. $1$
• C. $-2$
• D. $\infty$

Answer 1

Answer: (A)

$0$

Given, $f\left(x\right)=\cos x+\cos (\sqrt{2}.x)$
$f^{\prime }\left(x\right)=-\sin x-\sqrt{2}\sin (\sqrt{2}.x)$

Put $f^{\prime }\left(x\right)=0$, then
$x=0$ is the only one direction
$f^{\prime }\left(x\right)=-\cos x+\cos (\sqrt{2}.x)<0$ at $x=0$
Hence maxima occurs at $x=0$