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Exercise 3: The construction of a subroutine for the line search interpolation procedure.

a) Write a subroutine to construct the line search interpolation procedure described above once the values of and are provided. You can switch to the quadratic interpolant when the coefficient a is small or by examining the four values supplied.

b) Construct input data to cover all situations shown in Figure 7 and test your programs. Plot your results by showing your computed interpolant. Is your subroutine robust enough to produce a minimum in each case? How can it be improved?