# Thread: Finding CP using Partial Derivatives

1. ## Finding CP using Partial Derivatives

The equation is this
B = e ^(xy/2)

I have successfully found all 6 first and second order partial derivatives but need help finding the CP [/FONT]

2. I assume you mean critical point? If that's what you're talking about, then $(a,b)$ is a critical if $(a,b)$ is in the domain of $f(x,y)$ and:

1) $\frac{\partial f}{\partial x}(a,b)=\frac{\partial f}{\partial y}(a,b)=0$

OR

2) one or both of $\frac{\partial f}{\partial x}(a,b)$ and $\frac{\partial f}{\partial y}(a,b)$ are undefined.

In the case of $f(x,y)=e^{\frac{xy}{2}}$:

$\frac{\partial f}{\partial x}=\frac{ye^{\frac{xy}{2}}}{2}$
$\frac{\partial f}{\partial y}=\frac{xe^{\frac{xy}{2}}}{2}$

Knowing this, $(0,0)$ must be a critical point because $\frac{\partial f}{\partial x}=0$ when $y=0$. Similarly, $\frac{\partial f}{\partial y}=0$ when $x=0$. Since $e^{\frac{xy}{2}}$ can never equal $0$, the only critical point is $(0,0)$.