Apply Newton’s method (6S-accuracy). First sketch the function(s) to see what is going on.

Solve Prob. 5 by Newton’s method with x₀ = 5, 4, 1, -3. Explain the result.

Data from Prob. 5

Solve by fixed-point iteration and answer related questions where indicated. Show details.

Sketch f(x) = x³ - 5.00x² + 1.01x + 1.88, showing roots near ±1 and 5. Write x = g(x) = (5.00x² - 1.01x + 1.88)/x². Find a root by starting from x₀ = 5, 4, 1, -1. Explain the (perhaps unexpected) results.