$\text{ If }f\left(x\right)=\mathrm{maximum}\left\{x^3,x^2,\frac{1}{64}\right\}\mathrm{\forall }x\in [0,\mathrm{\infty }),\text{ then }$

• A

  $f\left(x\right)=\left\{\begin{array}{l}{x}^2,0\le x\le 1\\ x^3,x>1\end{array}\right.$

• B

  $f\left(x\right)=\left\{\begin{array}{l}\frac{1}{64},0\le x\le \frac{1}{4}\\ x^2,\frac{1}{4}<x\le 1\\ x^3,x>1\end{array}\right.$

• C

  $f\left(x\right)=\left\{\begin{array}{l}\frac{1}{64},0\le x\le \frac{1}{8}\\ x^2,\frac{1}{8}<x\le 1\\ x^3,x>1\end{array}\right.$

• D

  $f\left(x\right)=\left\{\begin{array}{l}\frac{1}{64},0\le x\le \frac{1}{8}\\ x^3,x>1/8\end{array}\right.$