How do you use Newtons method to solve for a functions optimum? I know that for finding the root you use:

For example lets say the function is: f(x) =X1 = X0 - f(X0)/f'(X0)

X2 = X1 - f(X1)/f'(X1)

X3 = X2 - f(X2)/f'(X2)

...etc4x^3-2x^2-5

What do you do differently to solve for optimum? My guess it has something to do with second derivative, but I'm not really sure. Any help would be appreciated

Thanks,

Brandon