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