Provide an appropriate response.Show that if h > 0, applying Newton's method to f(x) = leads to x2 = h if x0 = h and to x2 = -h if x0 = -h when 0 < 7 < h.

Question

What will be an ideal response?

Answer 1

f(x) = 

f '(x) = 

Let x₀ = h. Then,
x₁ = h -  = h - 2(h - 7) = 14 - h
x₂ = 14 - h +  = 14 - h + 2(h - 7) = h

Likewise, let x₀ = - h. Then,
x₁ = - h +  = - h + 2(7 + h) = 14 + h
x₂ = 14 + h -  = 14 + h - 2(h + 7) = - h