Provide an appropriate response.Use the Intermediate Value Theorem to prove that 3x4 - 2x3 + 7x - 5 = 0 has a solution between -2 and -1.

Question

What will be an ideal response?

Answer 1

Let f(x) = 3x⁴ - 2x³ + 7x - 5 and let y₀ = 0. f(-2) = 45 and f(-1) = -7. Since f is continuous on  and since y₀ = 0 is between f(-2) and f(-1), by the Intermediate Value Theorem, there exists a c in the interval (-2, -1) with the property that f(c) = 0. Such a c is a solution to the equation