Newton’s Method Consider the problem of locating the roots of the polynomial f(x) = 0. Newton’s method begins with a linear approximation to f(x) at x[1] as In the equation, we can use known values...

Newton’s Method Consider the problem of locating the roots

of the polynomial f(x) = 0. Newton’s method begins with a

linear approximation to f(x) at x[1] as

In the equation, we can use known values for x[1], f(x[1]), and the slope f′(x[1]) to determine point x, where f(x) = 0. As this is an iterative procedure, the second trial point is noted as x[2], where f(x[2]) = 0. Show yourself Newton’s method formula for x[2] is