设在 $[0,1]$ 上 $f^{\prime \prime}(x)>0$, 则下列顺序正确的是 ( ).
$\text{A.}$ $f^{\prime}(1)>f^{\prime}(0)>f(1)-f(0)$
$\text{B.}$ $f(1)-f(0)>f^{\prime}(1)>f^{\prime}(0)$
$\text{C.}$ $f^{\prime}(1)>f(1)-f(0)>f^{\prime}(0)$
$\text{D.}$ $f^{\prime}(1)>f(0)-f(1)>f^{\prime}(0)$