Thanks! Let f(x) = ~ - kx, fork > 0. Using a calculator or computer, sketch the

Question

Thanks!

Let f(x) = ~ - kx, fork > 0. Using a calculator or computer, sketch the graph off fork = 1/ 9, 1/ 6, 1/ 3, 1/ 2, 1, 2, 4. Describe what happens as k changes. f( x) has a local minimum. Find the location of the minimum. Find the y -coordinate of the minimum. Find the value of k for which this y-coordinate is largest. How do you know that this value of k maximizes they-coordinate? Find d2yj dl? to use the second-derivative test. (Note that the derivative you gel 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.)

Explanation / Answer

x = { ln(k/2)}/2

y = k{1 - ln (k/2) )/2

max at k = 1/9

the second derivate is -1/k which is negetive(since k is positive)

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