Let g be a differentiable function whose first derivative g′(x) is increasing for −2<x<1, attains a maximum at x=1, and is decreasing for 1<x<4. Which of the following must be true about g′′ at x=1?
a) g′′(1)=0 and changes sign from positive to negative at x=1.
b) g′′(1)=0 and changes sign from negative to positive at x=1.
c) g′′(1)>0.
d) g′′(1)<0.