A twice-differentiable function g is defined on [−3,5]. It is known that
• g(−3)=2,
• g(1)=7,
• g(5)=3, and
• g′(x)>0 for −3<x<1 while g′(x)<0 for 1<x<5.
Determine the absolute maximum value of g on the interval [−3,5] and the x-value where it occurs.