Question

Use Newton's method to approximate a root of the equation 2x³ + 3x + 3 = 0 as follows.

Let 1-1 be the initial approximation.
The second approximation 2 is
and the third approximation
3 is

Answer 1

Explanation:

Let f(x) = 2x³ + 3x + 3. Then f'(x) = 6x² + 3.

p(0) = 1.

p(1) = p(0) - f[p(0)]/f'[p(0)] = 1 - 8/9 = 1/9.

p(2) = p(1) - f[p(1)]/f'[p(1)] = -2183/2241.