If `f(x) = |cos x| + |sin x|`, then `dy/dx` at `x = (2pi)/3` is equal to

Options

A. `(1-sqrt(3))/(2)`
B. 0
C. `(1)/(2)(sqrt(3)-1)`
D. none of these

Explanation

In neighborhood of `x=(2pi)/(3),| cos x| = -cos x and | sin x| = som x`
`"or "y=-cos x+ sin x`
`therefore" "(dy)/(dx)=sin x + cos x`
Thus, at `x=(2pi)/(3)," we get "(dy)/(dx)= sin""(2pi)/(3)+cos""(2pi)/(3)=(sqrt(3)-1)/(2).`