The function g is continuous and differentiable on [0,4]. The slope of the secant line joining (0,g(0)) and (4,g(4)) is 21. At x=2, the tangent to the graph of g is horizontal. Which of the following must be true?
a) g′(x)=21 for all x in (0,4).
b) There exists at least one c in (0,4) such that g′(c)=21.
c) g′(x)>0 for all x in (0,4).
d) Because the interval midpoint is x=2, the Mean Value Theorem guarantees g′(2)=21.