1. Let $f(x)=x^{2}(2-x)$, then the interval of monotonic increase for $f(x)$ is
1. $\left(0, \frac{4}{3}\right) \quad f^{\prime}(x)=4 x-3 x^{2}$, from $f^{\prime}(x)>0$ we get $x \in\left(0, \frac{4}{3}\right)$.