mark
This is essentially problem 1.3.4 from our text. Note that problems 2, 3, and 5 are also great problems!
Let
f(x) = x^3 - 2x - 2.
- Write down the corresponding Newton’s method iteration function; call it N(x).
- Compute several iterates of N from x_0=0. What behavior do you see?
- Iterate N from several values of x_0 that are very close to zero (much smaller than 1 in absolute value). Now, what behavior do you see?
- Iterate N from a value larger than 1. Now what happens?
- Fire up our cobweb plot tool, plug in N(x), and an appropriate interval. How do your observations from the previous parts fit together with what is displayed by the cobweb plot?