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## Main Question or Discussion Point

Could anyone comment on the convexity of

f(x,y) = (x^2) * exp(y) ...... i.e. x square into e to the power y.

I did try to find Hessian of the same and the value I get is :

Hessian(x,y) = -2 * x^2 * exp(2y).... which looks <= 0 for all x and y.

I assume this should imply f(x,y) is concave. However when I plot this function using a 3D graph plotter it seems convex .

try

hp://ww.livephysics.com/ptools/online-3d-function-grapher.php

for plotting function.

I am sure I am making a simple mistake or something.

Any help would be useful.

f(x,y) = (x^2) * exp(y) ...... i.e. x square into e to the power y.

I did try to find Hessian of the same and the value I get is :

Hessian(x,y) = -2 * x^2 * exp(2y).... which looks <= 0 for all x and y.

I assume this should imply f(x,y) is concave. However when I plot this function using a 3D graph plotter it seems convex .

try

hp://ww.livephysics.com/ptools/online-3d-function-grapher.php

for plotting function.

I am sure I am making a simple mistake or something.

Any help would be useful.