Calculus 1
posted by Olivia .
Use Newton's method to approximate the root of the equation x^3+x+2=0 with initial guess x1=1 gives:

Using trig get:
Xn+1 = Xn  Yn/Y'n
where
Y = x^3 + x + 2
Y' = 3x^2 + 1
for x = 1
Y = 11+2 = 0 well how embarrassing, we guessed it exactly
Y' = 4 irrelevant