Posted by Eva on .
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 ycoordinate of the minimum.
y= _____
Find the value of k for which this ycoordinate is largest.
k= ______
How do you know that this value of k maximizes the ycoordinate? Find d^2y/dk^2 to use the secondderivative 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 ycoordinate of the minimum.)
MY ANSWERS ARE=
Loc. min= 1
ycoordinate=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...

Calculus Please Help 
Eva,
Oh... I got them... thanks anyways...