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Problem: secant method 2x^3-2x-5 [ Calculator, Method and examples ]

Solution:
Your problem -> secant method 2x^3-2x-5

Here 2x^3-2x-5=0

Let f(x) = 2x^3-2x-5

Here
 x f(x) 0 1 2 -5 -5 7

1^(st) iteration :

x_0 = 1 and x_1 = 2

f(x_0) = f(1) = -5 and f(x_1) = f(2) = 7

:. x_2 = x_0 - f(x_0) * (x_1 - x_0)/(f(x_1) - f(x_0))

x_2 = 1 - (-5) * (2 - 1)/(7 - (-5))

x_2 = 1.4167

:. f(x_2)=f(1.4167)=2*(1.4167)^3-2*(1.4167)-5=-2.147

2^(nd) iteration :

x_1 = 2 and x_2 = 1.4167

f(x_1) = f(2) = 7 and f(x_2) = f(1.4167) = -2.147

:. x_3 = x_1 - f(x_1) * (x_2 - x_1)/(f(x_2) - f(x_1))

x_3 = 2 - 7 * (1.4167 - 2)/(-2.147 - 7)

x_3 = 1.5536

:. f(x_3)=f(1.5536)=2*(1.5536)^3-2*(1.5536)-5=-0.6076

3^(rd) iteration :

x_2 = 1.4167 and x_3 = 1.5536

f(x_2) = f(1.4167) = -2.147 and f(x_3) = f(1.5536) = -0.6076

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