Use Newton's method to approximate a root of the equation 4 x^7 + 2 x^4 + 4 = 0 as follows. Let x _1 = 3 be the initial approximation. Carry at least 4 decimal places through your calculations.

Question

Use Newton's method to approximate a root of the equation  as follows.Let  be the initial approximation.The second approximation  is and the third approximation  is    Carry at least 4 decimal places through your calculations. find x_2 and x_3

Answer 1

Newton's method uses iteration to find the zero's of a function:

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

Start by plugging in x₁ = 3 into f(x) = 4x^7 + 2x^4 + 4 and into f'(x) = 28x^6 + 8x^3

get x₂ and repeat for x₃