Question

Using Newton-Raphs
f (x) = 2x3 + x2 - x + 1 accurate to within 10-4​

Answer 1

2x3+x2−x+1x

Explanation:

Let's solve for f.

fx=2x3+x2−x+1

Step 1: Divide both sides by x.

fx=2x3+x2−x+1x

fx=2x3+x2−x1x

Answer:

Answer 2

9514 1404 393

Answer:

-1.2338

Explanation:

The graph shows the one real root is about -1.234. The Newton's method iterator is ...

new x = x - f(x)/f'(x) . . . . . where f'(x) is the derivative of f(x)

Many graphing calculators provide a derivative function, so the iteration equation can be evaluated more or less directly by the calculator. In the attached, we have shown a table with three iterations of the root. After the second iteration, the root is good to 4 decimal places.

x ≈ -1.2338