If $g$ is a continuous function on the closed interval $-4,4$ and $g(-4)=2$ and $g(4)=7,$ which of the following statements is necessarily TRUE?

A$.$ The absolute maximum value for $g$ on $-4,4$ is $7$

B$.$ If $x,g(x)=0x-4,4gx-4,4g-4,4-4$ for $at$ least one value $ofx$

$C.,g(x)=0$ for $at$ least one value $ofxon$ the closed interval $-4,4$

$D.gis$ increasing for all $xon-4,4$

$E.$ The $absolute$ minimum value $ofgon-4,4is2$