Quick Calc question Newtons Method?

Question

use newtons method to approximate the value of cube root (59)

how would that translate into F(x)
so i would be able to use it in the formula

Answer 1

y = x^3-59
y'=3x^2
Guess root is 4
Then new root = 4 - f(4)/y'(4) = 3.8958333
You can repaet this until you get the accuracy you want
new root would be 3.895833- f(3.8958333)/y'(3.8958333)