- Can we use the IVT to conclude that f(x) = x3 + 2x + 1 passes through y = 0 on the interval (-2,2)?
Answer
Yes. For starters, f is continuous on the closed interval [-2,2]. We have a = -2 and b = 2, therefore

Since f(a) = -11 < 0 < 13 = f(b), the IVT says that there is some c with -2 < c < 2 and f(c) = 0.