设函数 $f(x)=\left\{\begin{array}{cl}x^\alpha \cos \frac{1}{x^\beta}, & x>0 \\ 0, & x \leq 0\end{array}(\alpha>0, \beta>0)\right.$ ，若 $f^{\prime}(x)$ 在 $x=0$ 处连续，则
A. $\alpha-\beta>1$
B. $0 < \alpha-\beta \leq 1$
C. $\alpha-\beta>2$
D. $0 < \alpha-\beta \leq 2$