A rectangle is bounded by the $x-$axis and the parabola $y=25-x^2.$ What length and width should the rectangle have so that its ares is a maximum?

The table below gives values of the contimuous function $f$ at selected values of $x.$

$\backslash$table$[[x,3,4,5,6,7],[f(x),10,12,9,5,8]]$

If $f$ has exactly two critical points on the open interval $(3,7),$ which of the following must be true?

$($A$)f(x)>0$ for all $x$ in the open interval $(3,7)$

$($B$)f^{\text{'}}(x)$ exists for all $x$ in the open interval $(3,7)$

$($C$)f^{\text{'}}(x)>0$ for all $x$ in the open interval $(3,7)$

$($D$)f^{\text{'}}(5)0$