The figure shows the graph of a function f Suppose that Newtons method is used to approximate the root s of the equation f (x) 0 with initial approximation x 1 6 (a) Draw the tangent lines that are used to find x 2 and x 3 , and estimate the numerical values of x 2 and x 3 (b) Would x 1 8 be a bett...

a The tangent line at x 1 6 intersects the xaxis at T ...

The figure shows the graph of a function f. Suppose that Newtons method is used to approximate

Question:

The figure shows the graph of a function f. Suppose that Newton’s method is used to approximate the root s of the equation f (x) = 0 with initial approximation x₁ = 6.
(a) Draw the tangent lines that are used to find x₂ and x₃, and estimate the numerical values of x₂ and x₃.
(b) Would x₁ = 8 be a better first approximation? Explain.