ISRO 2013- Newton Raphson [EE]

Question

The equation $x^3$ - $x^2$ + 4$x$ - 4 = 0 is to be solved using the Newton - Raphson method. If x =2 is taken as the initial approximation of the solution, then the next approximation using the method will be

a) 2/3

b) 4/3

c) 1/3

d) 5/3

Answer 1

f(X)=X³-X²+4X-4

f`(X)=3X²-2X+4

f(X₀)=8   f`(X₀)=12       (X₀=2)

X₁=2-$\frac{8}{12}$

X₁=4/3

Answer B.