Consider the function

f(x) = x 1

defined over the interval 2 x 6.

a. Perform three iterations of the three-point equal interval search by hand. What interval is guaranteed to contain the value of x that corresponds to the minimum of f after three iterations of the three-point equal interval search?

b. Perform one iteration of successive parabolic interpolation if f is sampled initially at x1 = 0,

x2 = 2, and x3 = 4. Based on this one iteration, at what value of x does f attain a minimum?