1. Using the quadratic formula, compute the roots of f (x) = 4x2 −3x −3. Show your work.
2. Implement bisection for root finding.
3. Transform the function f into an appropriate function g for a fixed point problem. Show your work.
4. Implement the fixed point method. Make sure you use good stopping criteria; see Sauer, section 1.2.4.
5. Using your implementations, compare the two root finding methods for finding the root of f . Which is faster? Can you find a function such that the other root finding method is faster? For f , you know the true roots. What if you didn’t know the true roots? How do you compute accuracy if you don’t know the true answer?
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