PLEASE SOLVE FOR X1 AND X2 ROUNDED APPROPRIATELY Write the formula for Newton\'s

Question

PLEASE SOLVE FOR X1 AND X2 ROUNDED APPROPRIATELY

Write the formula for Newton's method and use the given initial approximation to compute the approximations x_1 and x_2. f(x) = x^2 - 6x - 27, x_0 = 6 Write the formula for Newton's method for the given function. Choose the correct answer below. A. x_n + 1 = x_n - (x_n)^2 - 6(x_n) - 27/(x_n)^2 - 27 B. x_n + 1 = x_n - 2(x_n) - 6/(x_n)^2 - 6(x_n) - 27 C. x_n + 1 = x_n - (x_n)^2 - 6(x_n) - 27/2(x_n) - 6 D. x_n + 1 = x_n + (x_n)^2 - 6(x_n) - 27/2(x_n) - 6 Use the given initial approximation to compute the approximations x_1 and x_2. x_1 = (Do not round until the final answer. Then round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

xn+1 = xn - {(xn)2-6(xn)-27}/{(2xn)-6} ----------- (A)

Since we need to find x1 given that x0 = 1

SImply we will use equation (A)

assume n = 0 then formula will become:

x1 = x0 - {(x0)2-6(x0)-27}/{(2x0)-6}

put x0 = 6 to get our answer:

x1 = 6 - {36-36-27}/{12-6}

x1 = 6 - {-27/6} => 10.5 is our answer.

Similarily,

x2 = 10.5 - {20.25/15} => 10.5 - 1.35 => 9.15 is our answer

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