I'm trying to maximize an integral of a function that is itself an integral. I haven't used the constraint in my calculation, so I'm wondering if I have made a mistake. Any help would be appreciated.
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Mike
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I assume $C(t)$ is already defined. Take the partial derivatives of $\int_0^1 R(t)dt$ with respect to $k_{in}$ and $k_{out}$ and set them to zero and test for a maximum – fGDu94 Nov 28 '19 at 01:42
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C(t) is to be found. I need to maximize R(t) across all C(t) that have the integral =AUC. So, what C(t) maximizes the integral of R(t). – Mike Nov 28 '19 at 13:26
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I'm not sure but I think is not necessarily zero because $u'(u'^2-uu'')=\frac{u'}{u^2}(\frac{u'(u'^2-uu'')}{u^2})=\frac{u'}{u^2}(\ln(u)'')$ so what we want is solve $\ln(u)''=0$ – Dabed Dec 02 '19 at 09:51
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Thanks, but I was careless: L = kin(u + 1/kout)/u' – Mike Dec 04 '19 at 02:08