Let g be continuous on [0,5] and differentiable on (0,5) with g′(x)≥2 for all x in (0,5). Which of the following must be true on the interval (0,5)?
a) There exists c in (0,5) such that g′(c)=2.
b) The equation g(x)=7 has at most one real solution.
c) The equation g(x)=7 has at least one real solution.
d) There exists c in (0,5) such that g′(c)=0.