Let f(x) = ex- kx, for k > 0. Using a calculator or computer, sketch the graph of f for k changes. f(x) has a local minimum. Find the location of the minimum. X = Find the y-coordinate of the minimum. y = Find the value of k for which this y-coordinate is largest. k = = 1/9, 1/6, 1/3, 1/2, 1, 2, 4. Describe what happens as How do you know that this value of k maximizes the y-coordinate? Find d y/dk to use the second-derivative test. d'y dk (Note that the derivative you get is negative for all positive values of k, and confirm that you agree that this means that your value of k maximizes the y-coordinate of the minimum.) =