Question

Total number of values of '$x$' where the function $f\left(x\right)=\cos x+\cos \sqrt{2}x$ attains it's maximum value is/are

• A. $1$
• B. $2$
• C. $4$
• D. none of these

Answer 1

The correct option is A $1$

To find maxima and minima we have to find derivative

$f^{{}^{\prime }}\left(x\right)=-sinx-\sqrt{2}sin\sqrt{2}x$

$f^{{}^{\prime }}\left(x\right)=0$

so ,$-sinx-\sqrt{2}sin\sqrt{2}x=0$

so at only point at x=0,$f^{{}^{\prime }}\left(x\right)=0$

and$f^{{}^{\prime \prime }}\left(x\right)=-cosx-2cos\sqrt{2}x$

At x=0 , $f^{{}^{\prime \prime }}\left(x\right)=-cos0-2cos0=-3<0$

so at $x=0$ only one point when f(x) attains it's maximum value

so option${}^{\prime }{A}^{\prime }$ is correct.