Find the two $x-$intercepts of the function $f$ and show that $f^{\text{'}}(x)=0$ at some point between the two $x-$intercepts.

$f(x)=-8x\sqrt[\phantom{2}]{x+7}$

smaller $x-$value $(x,y)=$

larger $x-$value $,(x,y)=$

Find a value of $x$ such that $f^{\text{'}}(x)=0.$

$x=$