find an interval of length 0.5 containing a root of f(x) = x^3 +2x+1

Question



Answer 1

Let x₀ = - 0.5

x₁ = x₀ - (x₀³ + 2x₀ + 1)/(3x₀² + 2) = - 0.5 - (- 0.125)/(2.75) = - 0.45455 = - 0.4534

Tak kk f(- 0.5) = - 0.125 < 0 and f(0) = 1 > 0, then this interval is [- 0.5, 0]. It has length 0.5 and has at least one solution of this equation.