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

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

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

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

:. f'(x) = 6x^2-2

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

Here f(1) = -5 < 0 and f(2) = 7 > 0

:. Root lies between 1 and 2

x_0 = (1 + 2)/2 = 1.5

x_0 = 1.5

1^(st) iteration :

f(x_0)=f(1.5)=2*(1.5)^3-2*(1.5)-5=-1.25

f'(x_0)=f'(1.5)=6*(1.5)^2-2=11.5

x_1 = x_0 - f(x_0)/(f'(x_0))

x_1 = 1.5 - (-1.25)/(11.5)

x_1 = 1.6087

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