Find the interval in which the function $\displaystyle \mathrm{f}(x)=x^{4}-4 x^{3}+10$ is strictly decreasing.

$$\begin{aligned} & \mathrm{f}^{\prime}(x)=4 x^{3}-12 x^{2}=4 x^{2}(x-3) & \Rightarrow 4 x^{2}(x-3)<0 \text { for } x<3, x \neq 0 & \Rightarrow \mathrm{f}^{\prime}(x)<0 \text { for } x<3, x \neq 0 \end{aligned}Thus, $\displaystyle \mathrm{f}(x)=x^{4}-4 x^{3}+10$ is strictly decreasing on $\displaystyle (-\infty, 0) \cup(0,3)$.Thus, $\displaystyle \mathrm{f}(x)=x^{4}-4 x^{3}+10$ is strictly decreasing on $\displaystyle \left.(-\infty, 0] \cup[0,3]\right)$