1. Do 3 iterations of bisection by hand on  f(x) = x6 − 2 on [0,2].
   Give an upper bound for the error.
 
2. Consider the function    F(x) = x6 − x − 1 .
   We want to find its positive root(s). 

 a. Check that there is only one positive root. 
    
 b. What would be a good interval [a,b] for bisection (with integer endpoints) ? 

 c. Estimate how many bisection iterations it would take to find the root to 
    accuracy of 0.1 and of 0.001. 

 d. Use bisection, by hand (on a calculator!) to find the root to an accuracy 
    of 0.1  (it should not take more than 5 iterations).

 e. Use Newton-Raphson, by hand (on a calculator!) to find the root to an accuracy 
    of 0.1, with initial guess one of the endpoints from above. 
 	

 e. Use Secant method, by hand (on a calculator!) to find the root to an accuracy 
    of 0.1, with initial guesses x0, x1 the two (integer) endpoints.