A differentiable function g is summarized in the incomplete table below.
x
2
3
4
g(x)
5
—
13
g'(x)
3
—
7
Which statement about g at x=3 is most strongly supported by the data?
a) g is increasing at x=3 because g′(3) must be positive.
b) g′(3)=4 by the Mean Value Theorem.
c) No conclusion about the sign of g′(3) can be drawn from the given data.
d) g must have a local maximum at x=3.