Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. -f(x) = 3x³ - 6x + 2; [1, 2] A) f(1) = -1 and f(2) = -14; no B) f(1) = -1 and f(2) = 14; yes C) f(1) = 1 and f(2) = -14; yes D) f(1) = 1 and f(2) = 14; no

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The Intermediate Value Theorem states that if a function f is continuous on a closed interval [a, b] and N is any number between f(a) and f(b), then there exists at least one number c in the interval [a, b] such that f(c) = N. For the given function f(x) = 3x^3 - 6x + 2, evaluating f(1) = 3(1)^3 - 6(1) + 2 = -1 and f(2) = 3(2)^3 - 6(2) + 2 = 24 - 12 + 2 = 14. Since f(1) = -1 and f(2) = 14, and these values have opposite signs, there must be at least one zero in the interval [1, 2] according to the Intermediate Value Theorem.

Use the Intermediate Value Theorem to Determine Whether the Polynomial