Input a function f(x) and use Newton's method to approximate a root. [br][br]Here, f(x) = x^2 - 2, and the initial guess is x_1 = 3. [br][br]You can change the function using the input box (type "f(x) = x^4-4x^3", for example), and you can change the initial guess x_1 in spreadsheet cell b2.

Follow the first three iterations of Newton's method on the x-intercepts of the tangent lines to P_1, P_2, P_3. [br][br]Can you find a function for which Newton's method works, but takes more than 10 iterations? [br][br]Can you find a function for which Newton's method fails?