One of the best-known interpolation methods is Newton's Method, which exploits a quadratic approximation to the function f (x) at a given point x₁. The quadratic approximation q is given by:

a. Starting with x = 4 and a tolerance of ε = 0.01, use Newton's Method to minimize f (x) = x² + 2x, over –3≤ x ≤ 6.

b. Use Newton's Method to minimize:

Let the tolerance be " ε = 0.01 and start with x = 0.4.

c. Repeat part (b), starting at x = 0.6. Discuss what happens when you apply the method.