A twice-differentiable function g is defined on the closed interval [−2,4]. The derivative satisfies g′(x)>0 on (−2,1) and g′(x)<0 on (1,4), with g′(1)=0. Which x-value is most likely to be the location of the absolute maximum of g on [−2,4]?
a) x=0
b) x=1
c) x=−2
d) x=4