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I want to take derivative with respect to $p(t)$, but I am not sure if I can just assume $p(t)$ is another variable since it depends on $t$.

$$ \pi = \int_a^b p(t)\cdot \bigl(a-b\cdot p(t)\bigr)\cdot(u- v \cdot t)\, dt $$ Thanks

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    Then don't assume; just replace $p(t)$ with $p(t)+h \phi(t)$ where $\phi$ is a function and $h$ is a real number; evaluate the integral; differentiate the result with respect to $h$. You'll get the directional derivative in the direction $\phi$.2012-05-16
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    I am sorry, I am not clear what to do. I don't know the function form of p(t). What I am trying to do is to take derivative with respect to p(t) and equate that with zero to find the optimal function form for p(t). Would this clarification make any change in your response? Thanks2012-05-16

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