Let $f(x)={4x^3-3x^2\over6}-2\sin x+(2x-1)\cos x$ then $f(x)$

(1) decreases in $\left[{1\over2},\ \infty\right)$

(2) increases in $\left[{1\over2},\ \infty\right)$

(3) decreases in $(-\infty,\ \infty)$

(4) increases in $\left(-\infty,\ {1\over2}\right]$

(1) decreases in $\left[{1\over2},\ \infty\right)$

(2) increases in $\left[{1\over2},\ \infty\right)$

(3) decreases in $(-\infty,\ \infty)$

(4) increases in $\left(-\infty,\ {1\over2}\right]$