By using x0 = 0.49 the value goes to more than 1.
Given function f(x) = x³- sinx
By newton's method x₀ = 0.49
Formula for the newton's method is
Xₙ₊₁ = Xₙ - f( Xₙ)/ f'( Xₙ)
X₀ = 0.49,f(x) = x³- sinx and f'(x) = 3x²- cosx
X₁ = X₀ - f( X)/ f'( X)
X₁ = 0.49 - x³- sinx/3x²- cosx
X₁ = 0.49-(0.49)³-sin(0.49)/3(0.49)²-cos(0.49)
X₁ = 0.658
X2 = X1 - f(X₁)/ f'(X₁)
By substituting the values we get,
X2 = 1.012
So, Using x0 = 0.49 the value goes to more than 1.
To learn more about Newton's method click here:
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