# Math Help - Tricky stationary points

1. ## Tricky stationary points

What are the stationary points of

f(x,y) = e^((-x^3) +3x (-y^2))

and determine their nature.

Right, so the partial derivative holding y constant is:

((-3x^2) + 3 (-y^2))e^((-x^3) +3x (-y^2))

and holding x constant:

((-x^3) + 3x -2y)e^((-x^3) +3x (-y^2))

Is that correct?
If so, I make them equal to zero?
And then find the second partial derivative to determine the nature of the stationary points?

How the hell do I do that, im not sure im doing it right..

And apologies for the untidiness of the functions.

2. Originally Posted by BogStandard
What are the stationary points of

f(x,y) = e^((-x^3) +3x (-y^2))

and determine their nature.

Right, so the partial derivative holding y constant is:

((-3x^2) + 3 (-y^2))e^((-x^3) +3x (-y^2))

and holding x constant:

((-x^3) + 3x -2y)e^((-x^3) +3x (-y^2))

Is that correct?
If so, I make them equal to zero?
And then find the second partial derivative to determine the nature of the stationary points?

How the hell do I do that, im not sure im doing it right..

And apologies for the untidiness of the functions.
$f(x,y) = e^{-x^3 -3x y^2}$

$
f_x(x,y)=(-3x^2-3y^2)e^{-x^3 -3x y^2}=-3(x^2+y^2)e^{-x^3 -3x y^2}
$

$
f_y(x,y)=(-6xy)e^{-x^3 -3x y^2}
$

RonL