The graph of a differentiable function g is described as follows:
• g is decreasing on (0,2) and (4,6).
• g is increasing on (2,4).
• The tangent line to g is horizontal at x=2 and at x=4.
Which of the following sign charts for g′ on (0,6) is consistent with this information?
a) g′>0 on (0,2), g′=0 at x=2, g′<0 on (2,4), g′=0 at x=4, and g′>0 on (4,6).
b) g′<0 on (0,2), g′=0 at x=2, g′>0 on (2,4), g′=0 at x=4, and g′<0 on (4,6).
c) g′>0 on (0,2), g′=0 at x=2, g′>0 on (2,4), g′=0 at x=4, and g′<0 on (4,6).
d) g′<0 on (0,2), g′=0 at x=2, g′>0 on (2,4), g′=0 at x=4, and g′>0 on (4,6).