Let f(x)=e^(2x)-kx, for k greater than 0.
Using a calculator or computer, sketch the graph of f for k=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 the y-coordinate? Find d^2y/dk^2 to use the second-derivative test.
(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.)
MY ANSWERS ARE=
Loc. min= 1
k where y is largest= 2
d^2y/d^2k = 4e^(2x)
The only one I got right plugging in these values was k when y is largest...