Newton's method for root finding

There is only one steady current through the tunnel diode with the given characteristic I = I(V) and a resistor R = 19.2 under the applied voltage source E = 1.8 (see the figure again). The voltage value for the root is

V* = 0.880133

The Newton method xk+1 = xk - f(xk) / f'(xk) is stable and rapidly converges to the root if an initial value V0 is sufficiently close to V* (notice that the contraction mapping method would always diverge for the root). The error errk defined as the distance |Vk-V*| is plotted in the example below (red dots). After a few intermediate iterations, the error exhibits the quadratic convergence according to the theory.

Enter an initial approximation of the root:


Possible initial values for your choice: -2, -1, 0, 1, 2, and 3. Notice that the interval for convergence of the Newton's method is rather wide.