Provide an appropriate response.Use the Intermediate Value Theorem to prove that 5x4 + 8x3 + 8x - 1 = 0 has a solution between -3 and -2.

Question

What will be an ideal response?

Answer 1

Let f(x) = 5x⁴ + 8x³ + 8x - 1 and let y₀ = 0. f(-3) = 164 and f(-2) = -1. Since f is continuous on  and since y₀ = 0 is between f(-3) and f(-2), by the Intermediate Value Theorem, there exists a c in the interval (-3, -2) with the property that f(c) = 0. Such a c is a solution to the equation