Write programs to solve for the positive root of

Question 1.6 -

The function * f(x)=*tanh * x* has a root at * x*=0.
Write a program to show that the Newton-Raphson method does not converge
for an initial guess of * x * very much larger than 1.
Can you understand what is going on by considering a graph of tanh*x*?
From the explicit form
of (1.14) for this problem, derive the critical value of the initial
guess above which convergence will not occur?
Try to solve th eproblem using the secant method. What happens for various initial guesses if you try to find the * x *=0 root of tan*x*
using either method.

The extra material for Question 2 includes questions
and the description of the Henon-Heiles model
here