Question

X5 − x − 7 = 0, x1 = 1

Answer 1

Define the tangent line equation at the given point; and find its x intercept. use that x intercepts as a new guess for X, and repeat and tangent y = f'(a)(x-a) + f(a) 0 = f'(a)(x-a) + f(a) 0 - f(a) = f'(a)(x-a) - f(a)/ f'(a) = x-a a - f(a)/ f'(a) = x ...X_2=1-\frac{1^5-1-7}{5(1)-1}.