Use Newton's Method to approximate the zero(s) of the function.

Question

Continue the iterations until two successive approximations differ by less than 0.001. Then find the zero(s) to three decimal places using a graphing utility and compare the results.

f(x) = 2 − x³

^{Newton's Method:}

^x=

^{Graphing Utility}

^x=

Answer 1

Newton's method is x_n = x_n-1 - f(x_n-1)/f'(x_n-1) starting with x₀ = guess like 1

You need to calculate f'(x) = -3x²

first iteration: x₁ = 1 - 1/(-3) = 1.3333333333 and keep going until the change in x is less than .001

For second part, go to Desmos.com and type in y=2-x^3 and hover over the dot on the x axis where the zero is. The coordinates will be given. If it doesn't have enough sig figs, use the wrench on upper right to change your window. You can do the same on a Graphing calculator.