Verified answer

f(x) = 7 - 2x^2 + 2^-x

f '(x) = -4 x - (2^(-x)) ln(2)

guess x = -4

xn+1= y(xn)-y(xn)/y'(xn)

y= 7 - 2 * x ^ 2 + 2 ^ (-x)

y'= -4*x-2^(-x)*LN(2)

0 -4 -9 +4.90965 -1.83313

1 -2.16687 +2.09981 +5.55492 +0.37801

2 -2.54488 -0.11725 +6.13460 -0.01911

3 -2.52577 -0.00022 +6.11138 -0.0000361

x = -2.52577

guess x = 2

N x______ y______ y'______ y/y'______

0 +2 -3/4 -8.17329 +0.09176

1 +1.90824 -0.01632 -7.81762 +0.00209

2 +1.90615 -8.4E-06 -7.80953 +1.08089E-06

x=1.90615

N x______ y______ y'______ y/y'______

0 -10 +831 -669.78271 -1.24070

1 -8.75930 +286.87239 -265.31944 -1.08123

2 -7.67807 +93.89367 -111.24362 -0.84404

3 -6.83403 +27.68211 -51.74505 -0.53497

4 -6.29906 +6.38553 -29.38341 -0.21732

5 -6.08174 +0.75567 -22.62045 -0.03341

6 -6.04833 +0.01579 -21.67947 -0.00073

7 -6.04761 7.368E-06 -21.65923 -3.40187E-07

x=-6.04761