Question

Using Newton’s method to find the zero of the function f(x)=x^5−3x^3+1 using x_0=0.7, which of the following best represents the value of x_2?

Answer 1

Newton's method is an iterative method for finding the roots of a function. Given a function f(x) and an initial guess x_0 for a root of the function, Newton's method generates a sequence of approximations x_1, x_2, x_3, ... to the root of the function according to the following formula:

x_{n+1} = x_n - f(x_n)/f'(x_n)

To find x_2 using Newton's method, you would use the initial guess x_0 = 0.7 and apply the formula twice. The first iteration would give you x_1, and the second iteration would give you x_2.

If you plug in the values given in the problem (f(x) = x^5 - 3x^3 + 1, x_0 = 0.7) and perform the iterations, you will find that x_2 is approximately 0.72488.

Explanation: