Find the value of `a` in order that `f(x)=sqrt(3)sinx-cosx-2a x+b` decreases for all real values of `xdot`

Options

A. `alt1`
B. `age1`
C. `agesqrt(2)`
D. `altsqrt(2)`

Answer

B

Explanation

For `f(x)` to be decreasing `f'(x) lt 0 AA x epsilonR`
`implies sqrt(3)cos x +sin x-2alt0,AA xepsilonR`
`implies (sqrt(3))/2 cos x+1/2 sin x lt a, AA x epsilonR`
`implies sin(x+pi//3)lt a, AA x epsilonR `
`implies a ge1 [ :' sin (x+pi//3) le1]`