The polynomial function p(x)=x3−4x−1 is continuous for all real x. Which of the following justifies whether the equation p(x)=2 has at least one real solution in the interval (1,3)?
a) Yes; p is continuous on [1,3] and p′(1)<2<p′(3).
b) No; both p(1) and p(3) are greater than 2, so the equation has no solution in (1,3).
c) Yes; p is continuous on [1,3] and p(1)<2<p(3).
d) Yes; p(2)=1<2, so the equation must have a solution near x=2.