The number of values of `x` where the function `f(x)=cosx+cos(sqrt(2)x)` attains its maximum is 0 (b) 1 (c) 2 (d) infinite

Options

A. 1
B. 0
C. 2
D. infinite

Answer

A

Explanation

Given `f(x)=cosx+cos sqrt(2)x`

`impliesf'(x)=-sinx -sqrt sin sqrt(2)x`
and `f''(x)=-cosx-2cos sqrt(2)x`
For maximum or minimum put `f'(x)=0`
`implies-sin x-sqrt(2)x=0impliesx=0`
At `x=0, f''(x)lt0` maxima
`:.f(x)` is maximum only once.