is a constant, so we can pull it out, getting . Use the product rule to differentiate , set , and then plug in for . Now, solve for .
Find the value of k so that f(x)=xe^x/k has a critical value at x=10.
I am pretty sure I have to find the derivative here, using the product rule? But I'm not exactly how to find the derivative of e^x/k and after that I'm not sure what to do. Set the derivative equal to 10 perhaps? Someone help me clear this up, please.
Thank you very much. There are a couple of other problems I'm having trouble with as well.
"The quantity of a drug in the bloodstream t hours after a tablet is swallowed is given by: q(t) = 351(e^-t - e^-2t) in milligrams
When is the quantity of the drug in the bloodstream maximized? That is, find the value of t that maximizes q(t). Round your answer to two decimal places."
This is a surge function problem, but it's not in the normal format of ate^-bt that I'm used to working with. I can do (1/b) to find t, but I don't know how to find b. My first thought would be to combine e^-t - e^-2t to find b but I'm not sure if I can combine those just because they have the same base.
Also, for part of a problem I need the derivative of e^-kt, would that just be -ke^-kt? Or is k positive?