Question

Write Newton's formula used to approximate a solution of the equation 2x^3 - x - 15 = 0 and find the third iteration value. Be sure to verify both parts of the answer are correct when making your selection.

Answer 1

The formula used to approximate a solution of the equation 2x^3 - x - 15 = 0 is Newton's method. To find the third iteration value, start with an initial guess and perform the iteration process three times using the Newton's method formula.

Step-by-step explanation:

The formula used to approximate a solution of the equation 2x^3 - x - 15 = 0 is Newton's method. The formula for Newton's method is:

x(n+1) = x(n) - f(x(n))/f'(x(n))

where x(n) is the nth iteration value, f(x(n)) is the value of the function 2x^3 - x - 15 at x(n), and f'(x(n)) is the derivative of the function at x(n).

To find the third iteration value, we need to start with an initial guess for x(0) and perform the iteration process three times:

1. Choose an initial guess x(0)
2. Calculate f(x(0)) and f'(x(0))
3. Calculate x(1) using the formula x(1) = x(0) - f(x(0))/f'(x(0))
4. Repeat steps 2 and 3 to calculate x(2) and x(3)