Find $x=c$ guaranteed by the Mean Value Theorem when applied to $f(x)=x^3$ on the interval $1,3.$

$($A$.)c=13$

$($B$.)c=\sqrt[3]{13}$

$($C$.)c=\sqrt[3]{26}$

$($D$.)c=\sqrt[\phantom{2}]{\frac{13}{3}}$

$($E$.)c=0$