Posted by **Eva** on Wednesday, April 6, 2011 at 10:43pm.

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.

x= ____

Find the y-coordinate of the minimum.

y= _____

Find the value of k for which this y-coordinate is largest.

k= ______

How do you know that this value of k maximizes the y-coordinate? Find d^2y/dk^2 to use the second-derivative test.

d^2y/d^2k=

(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

y-coordinate=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...

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