MATH116 Lecture Notes - Lecture 2: Negative Number
9 Dec 2015
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Tutorial solutions 6: suppose that we know that f (x) is continuous and di erentiable on [4, 10]. Suppose that we also know that f (4) = 6 and that f(cid:48)(x) 4. It is given that f is continuous and di erentiable on [4, 10], so we may apply the mean value. Thus there exists some c (4, 10) such that f(cid:48)(c) = f (10) f (4) 6 since it"s given that f(cid:48)(x) 4, then we can say that. 4 f (10) + 6 24 f (10) 24 6 f (10) 18: starting with an initial guess of x0 = 2, use newton"s method to approximate 3. Stop the iterations when your approximations converge to four decimal places of accuracy. Compare with the approximation provided by your calculator. We are looking to approximate the root of f (x) = x3 7 = 0. Newton"s method takes the form: xn+1 = xn f (xn) f(cid:48)(xn)
