You are asked to solve a nonlinear equation f(x) = 0 on the interval [1, 5] using Newton's method. Tick ALL of the follo

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You Are Asked To Solve A Nonlinear Equation F X 0 On The Interval 1 5 Using Newton S Method Tick All Of The Follo 1 (49.66 KiB) Viewed 60 times

You are asked to solve a nonlinear equation f(x) = 0 on the interval [1, 5] using Newton's method. Tick ALL of the following that are true: This iterative method requires one starting point. This iterative method requires two starting points. This iterative method requires evaluation of derivatives of f. This iterative method does not require evaluation of derivatives of f. This iterative method requires the starting point(s) to be close to a simple root. This iterative method does not require the starting point(s) to be close to a simple root. If f = C([1,5]) and ƒ(1)ƒ(5) <0, then, with the starting point x₁ = 3, this iterative method converges linearly with asymptotic constant 3 = 0.5. If f(x) = 0 can be expressed as a = g(x), where g = C¹([1,5]) and there exists K = (0, 1) such that g'(x)| ≤ K for all x = (1,5), then this iterative method converges linearly with asymptotic constant <K for any starting point x₁ = [1, 5]. If f = C² ([1,5]) and the starting point is sufficiently close to a simple root in (1,5), then this iterative method converges quadratically. If f = C²([1, 5]) and the starting points ₁ and ₂ are sufficiently close to a simple root in (1,5), then this iterative method converges superlinearly with order v1.6.