Provide an appropriate response.Use the Intermediate Value Theorem to prove that -2x4 - 5x3 - 3x - 9 = 0 has a solution between -2 and -1.

Question

What will be an ideal response?

Answer 1

Let f(x) = -2x⁴ - 5x³ - 3x - 9 and let y₀ = 0. f(-2) = 5 and f(-1) = -3. 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