Respuesta :
Answer:
The value of [tex]x_2=-1.6923[/tex].
Step-by-step explanation:
Consider the provided information.
The provided formula is [tex]f(x)=x^3+x+6[/tex]
Substitute [tex]x_1=-2[/tex] in above equation.
[tex]f(x_1)=(-2)^3+(-2)+6[/tex]
[tex]f(x_1)=-8-2+6[/tex]
[tex]f(x_1)=-4[/tex]
Differentiate the provided function and calculate the value of [tex]f'(x_1)[/tex]
[tex]f'(x)=3x^2+1[/tex]
[tex]f'(x)=3(-2)^2+1[/tex]
[tex]f'(x)=13[/tex]
The Newton iteration formula: [tex]x_2=x_1-\frac{f(x_1)}{f'(x_1)}[/tex]
Substitute the respective values in the above formula.
[tex]x_2=-2-\frac{(-4)}{13}[/tex]
[tex]x_2=-2+0.3077[/tex]
[tex]x_2=-1.6923[/tex]
Hence, the value of [tex]x_2=-1.6923[/tex].
