Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line $,.$

$f(x)=x+\frac{16}{x}$;$[-7,-1]$

Absolute maximum: $-8,$ absolute minimum: $-\frac{65}{7}$

Absolute maximum: $-8,$ absolute minimum: $-17$

Absolute maximum: $-8,$ absolute minimum: $-15$

Absolute maximum: $-\frac{65}{7},$ absolute minimum: $-17$