[1] The 111eehanjos rule for approximating square roots states that a .1}, +1 where 1 a J'n+1 = 5(1'11 + } - In for n : 1. 2. 3. and .1'1 is any positive approximation to J5. (a) Apply Newton's Method to f(1) = 1"\") u to derive the 111eehanic's rule. [b] Use the mechanics rule to approximate 13. (2] Use Newton's Method to approximate the global 111aximum of f (.r) = .r cos I on the interval [0- 5]