Let f(x)=x3−6x+1. Which of the following statements about the equation f(x)=0 on the interval [0,2] is true?
a) Exactly two distinct real solutions occur on [0,2] because f changes concavity within the interval.
b) There is at least one real solution on [0,2] because f(0)=1 and f(2)=3 are both positive.
c) There is at least one real solution on [0,2] because f(0)=1 and f(2)=−3 have opposite signs.
d) There is no real solution on [0,2] because f is decreasing on that interval.