Determine the range of values by steepest-descent algorithm

Question

Response to the following problem:

Consider the performance index

J= h² + 40h + 28

Suppose that we search for the minimum of J by using the steepest-descent algorithm

h(n + 1) = h(n) - 1/2 Δg(n)

where g(n) is the gradient.

a. Determine the range of values of ? that provides an over damped system for the adjustment process.

b. Plot the expression for J as a function of n for a value of ? in this range.