1. Use Newton's method to approximate a root of f(x) = −x³ − 4x² + 2x − 6 starting at xo = 1 and give the exact value of x3. -

Use Newton's method to find the zeros of f(x) = 4x² - 4x² using the given starting values in (a) through (c). (a) xo = -1.5 and Xo = - 0.9, lying in = O A. For Xo = B. For Xo -1.5 and Xo 1.5 and Xo √2 (-∞, -1/2) == - 0.9, Newton's method does not converge. The values of x; alternate between 1.5 and 0.9 as i increases. == -0.9, X₁→ as i gets large.

14. Use Newton's method to find the root of the equation x5 – 3x4 + 7x² – 3x – 2 = 0 in the closed interval [-1,0]. For x1 = -0.5, find x2 and x3 and sketch the graph. Round to three decimal places.

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