For each of your root finding implementations, find roots of the following two functions:

1. f 1(x) = cos(x) x with the x initial bracket [0,1]

2. f 2(x) = tanh(x ) with the x initial bracket [10, 10]

Make a comparison table for these algorithms with the following rows:

1. Method name 2. Root of f 1(x) 3. Initial bracket or starting value used for f 1 4. Number of iterations to solve f 1 5. Root of f 2(x) 6. Initial bracket or starting value used for f 2 7. Number of iterations to solve f 2

If an algorithm diverges with the suggested initial bracket, indicate this, appropriately modify the bracket, and show the modified bracket in the above table as well. State your conclusions about the speed and robustness of the methods.