Heavy Lifting  thoughts and web finds by an economist 
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Saturday, July 17, 2010
This from imgur: Cool.
Comments:
The explanation (the payoffvscost curve is a downward pointing parabola) is basically correct.
The equations you present, while correct, do not explain what's happening to someone not already familiar with calculus and analytic geometry.
you are correct. in an undergraduate class we will work through the graphical depiction of what is happening in this problem, using a lot of words to explain exactly what is going on. Then we replace multiple boards' worth of discussion with three elegant lines of calculus to reach the same answer. This is often when students in economics understand how important their differential calculus class was supposed to be.
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