Suppose the tangent line to the curve y = f(x) at the point (1, 3) has the equation y = 7 − 4x.

Question

If Newton's method is used to locate a solution of the equation f(x) = 0 and the initial approximation is x1 = 1, find the second approximation x2.

Answer 1

The fact that (1,3) is on the graph of f means f(1) = 3.

The equation of the tangent line tells you that the slope is -4 which means f'(1) = -4.

Newton' method indicates that x₂= x₁- f(x₁)/f'(x₁). Take it from there given that x₁=1.