# Maximizing/Minimizing triangle area

I think I set it up right and I know area of a triangle is 1/2(BH). So I get 1/2(xy) and then try to maximize/minimize X? What do I plug in for Y?

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Please use parentheses when using the slash for division. Sometimes when we see $1/2(BH)$ it means $\frac 1{2BH}$, sometimes (as here) it means $\frac {BH}2$. Either $BH/2$ or $(1/2)BH$ or \frac {BH}2 between dollar signs to get the stacked fraction (preferred). Some hints are here –  Ross Millikan Nov 23 '13 at 4:18

Since the point is on the curve $y=\exp(\frac {-x}3)$ that is what you should use for $y$. Then you can maximize over $x$.

Added: The area of the triangle is $A=\frac 12x\exp(\frac {-x}3)$ Then $\frac{dA}{dx}=\frac 12\left( \exp(\frac{-x}3)-\frac x3\exp(\frac{-x}3)\right)$ Does that help?

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