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For the function F(x) = find minimum value using two methods - a. Newton's method starting...

For the function F(x) = x^{^{4}} -14 x^{^{3}} +60 x^{^{2}}-70 x find minimum value using two methods -

a. Newton's method starting with initial point of 1

b. Golden section in the interval [0,2]

required tolerance =0.001

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Answer #1

Solution Given, F(x) = x - 14x² + 60 x? - 70x as Newtons method. xo = 1 f(x) = 40c3 _ 42 x² + 1200-70 Newtons method formIteration 4 ; n = 3 Xч li OC f (x₂) pa) (1.922334 14(1.99833460(1.9223) ?- 70 (1.9223) 4 (1.9223)3 - 4 R I 1.9223)2 +1Q6(1.92

golden section method d=0.618034*(b-a) x1-ad x2-b-d check-if(abs(x2-x1)<0.001 than 1 else 0) . f(x) = x^4 - 14x^3 + 60x^2 - 7

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