Develop an M-file to implement parabolic interpolation to locate a minimum. The function should have the following features: Base it on two initial guesses, and have the program generate the third initial value at the midpoint of the interval. Check whether the guesses bracket a maximum. If not, the function should not implement the algorithm, but should return an error message. Iterate until the relative error falls below a stopping criterion or exceeds a maximum number of iterations. Return both the optimal x and f(x). Test your program with the same problem as Example 7.3. Consider the following function: f(x) = 3 + 6x + 5x^2 + 3x^3 + 4x^4 Locate the minimum by finding the root of the derivative of this function. Use bisection with initial guesses of x_l = -2 and x_u = 1