a) Graph the function: f(x) = x + 2x + 8x + 5x b) Does the...

 

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a) Graph the function: f(x) = x + 2x + 8x + 5x b) Does the function in (a) have a minimum for -2 < x < 1? Use an analytical method to support your answer. c) Find the location of the minimum of the function in (a) (i.e. the value of x at which the function reaches a minimum value) using golden-section search with x = -2, xu = 1. Perform fifteen iterations. Calculate values to four decimal places. What is the minimum of the function at this point? Show the first three iterations of calculations by hand and then use Excel or MATLAB to generate the remaining values for a presentation in a table. d) Find the minimum value of the function in (a) using parabolic interpolation with initial points x = -2, x = -1, and x3 = 1. Perform five iterations and calculate values to four decimal places. a) Graph the function: f(x) = x + 2x + 8x + 5x b) Does the function in (a) have a minimum for -2 < x < 1? Use an analytical method to support your answer. c) Find the location of the minimum of the function in (a) (i.e. the value of x at which the function reaches a minimum value) using golden-section search with x = -2, xu = 1. Perform fifteen iterations. Calculate values to four decimal places. What is the minimum of the function at this point? Show the first three iterations of calculations by hand and then use Excel or MATLAB to generate the remaining values for a presentation in a table. d) Find the minimum value of the function in (a) using parabolic interpolation with initial points x = -2, x = -1, and x3 = 1. Perform five iterations and calculate values to four decimal places.