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Pulty
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\(\displaystyle f(x,y) = \frac{1}{2}{x}^{2}{e}^{y}-\frac{1}{3}{x}^{3}-y{e}^{3y}\)
To start off I found the partial derivatives of
\(\displaystyle x: {e}^{y}x - {x}^{2}\)
\(\displaystyle y: \frac{{e}^{y}{x}^{2}}{2}-{e}^{3y}-3{e}^{3y}y\)
Then solved simultaneously for each equation equal to 0.
\(\displaystyle y = \ln(x) = -\frac{1}{6}\)
\(\displaystyle x = {e}^{-\frac{1}{6}}\)
(Is there another stationary point?)
I'm unsure of where to go from here, or if I'm even doing the right thing to begin with.
Thank you
To start off I found the partial derivatives of
\(\displaystyle x: {e}^{y}x - {x}^{2}\)
\(\displaystyle y: \frac{{e}^{y}{x}^{2}}{2}-{e}^{3y}-3{e}^{3y}y\)
Then solved simultaneously for each equation equal to 0.
\(\displaystyle y = \ln(x) = -\frac{1}{6}\)
\(\displaystyle x = {e}^{-\frac{1}{6}}\)
(Is there another stationary point?)
I'm unsure of where to go from here, or if I'm even doing the right thing to begin with.
Thank you
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