Let . Which of the following statements about the equation on the interval is…
MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
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.