Newton Raphson question

[trolluser]

Find the root of the function y = x
3 + 4x
2 + 7 in the vicinity of x = −4 correct to 5
decimal places.


I have got so far:


Let f(x)= x^3+4x^2+7


f'(x)= 3x^2+8x


Xn+1= Xn-f(xn)/f'(xn) => Xn+1= Xn-x^3-4x^2+7/3x^2-8x


x=-4, -4-(-4^3+4x-4^2+7)/(3x-4^2-8x-4)= -4.0875


On the right track?

 

[Ishuda]

Find the root of the function y = x
3 + 4x
2 + 7 in the vicinity of x = −4 correct to 5
decimal places.


I have got so far:


Let f(x)= x^3+4x^2+7


f'(x)= 3x^2+8x


Xn+1= Xn-f(xn)/f'(xn) => Xn+1= Xn-x^3-4x^2+7/3x^2-8x


x=-4, -4-(-4^3+4x-4^2+7)/(3x-4^2-8x-4)= -4.0875


On the right track?

Your initial function
X_n+1= X_n-f(x_n)/f'(x_n)
is correct but you seem to have messed up in the conversion when you substituted for f and f'. You should have
\(\displaystyle x_{n+1}\, =\, x_n\, -\, \frac{x_n^3\, +\, 4\, x_n^2\, +\, 7}{3\, x_n^2\, +\, 8\, x_n}\)
or with x_n = -4
\(\displaystyle x_{n+1}\, =\, -4\, -\, \frac{(-4)^3\, +\, 4\, (-4)^2\, +\, 7}{3\, (-4)^2\, +\, 8\, (-4)}\)