If f(x) is continuous in the interval [−1,1], f(−1)=4, and f(1)=6, can we use the Intermediate Value Theorem to conclude that f(c)=5 where −1< c <1?

Answer 1

Since f(x) is continuous on the interval [-1,1] and since f(-1) = 4 < 5 and since f(1) = 6 > 5, then according to the Intermediate Value Theorem, there is at least one number c in the interval (-1,1) for which f(c) = 5.