Maximizing problem (derivative of function related to water flow)

bjing

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Sep 26, 2018
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Greetings.

I have a problem related to the discharge of water flow in a channel.
The problem is as the attachment states (explanation; P=wetted perimeter= the channel "line" that is in contact with water, A=2d water area).
My initial plan was to follow the hint.
My calculations then gave
A=bd+md2 (=bd/2+kd(1+m2)0.5)**
and P=b+2d(1+m2)0.5, which yields
P=A/d+d(2(1+m2)0.5-m)
I was then thinking of taking the derivative of this function With respect to d, but my problem lies with the relationship between k,d and m. I have also tried to use ** in some way, but I can't come to a solution.

Thanks in advance for all tips and tricks.
 

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