Use Newton's method to approximate a root of the equation 2x3+3x+3=0 as follows.

Question

Use Newton's method to approximate a root of the equation 2x³+3x+3=0 as follows.

Let x₁ =−1 be the initial approximation.

The second approximation x₂ is ______

and the third approximation x₃ is ______

Answer 1

x_n+1=x_n-f(x)/f'(x)

f(x)=2x³+3x+3

f'(x)=6x²+3

x₁=-1

x₂=-1-f(-1)/f'(-1) = -1+2/9 = -0.777777777

x₃=-0.777777777+0.27/0.63 ≈ -0.736

If you graph f(x), when y=0, x≈ -0.7351