MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity
Problem
A function f is defined on an interval [a,b]. Which of the following statement(s) is/are incorrect?
(a) If f(a) and f(b) have opposite signs, then there must be a point c∈(a,b) such that f(c)=0.
(b) If f is continuous on [a,b], f(a)<0 and f(b)>0, then there must be a point c∈(a,b) such that f(c)=0.
(c) If f is continuous on [a,b], then there is a point c in (a,b) such that f(c)=0. Then f(a) and f(b) have opposite signs.
(d) If f has no zeroes on [a,b], then f(a) and f(b) have the same sign.