$\frac{\text{d}y}{\text{d}x}=\frac{-\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}$

$\frac{\text{d}y}{\text{d}x}=\frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}$

$\frac{\text{d}y}{\text{d}x}=\frac{-\frac{\partial f}{\partial y}}{\frac{\partial f}{\partial x}}$

 $-\frac{\left(x^2-y\right)}{\left(y^2+x\right)}$  

 $-\frac{\left(x^2+y\right)}{\left(y^2+x\right)}$  

 $\frac{\left(x^2-y\right)}{\left(y^2+x\right)}$  

$\frac{\partial\left(u,v,w\right)}{\partial\left(u,v,w\right)}=1$

$\frac{\partial\left(u,v,w\right)}{\partial\left(x,y,z\right)}=1$

$\frac{\partial\left(u,v,w\right)}{\partial\left(x,y,z\right)}=0$

 $\theta$  

 $r$  

 $r^2$  

$f\left(a,b\right)\ is\ \max imum\ value\ if\ AC-B^2>0\ and\ A>0\ or\ B>0$

$f\left(a,b\right)\ is\ \max imum\ value\ if\ AC-B^2>0\ and\ A<0\ or\ B<0$

$f\left(a,b\right)\ is\ \min imum\ value\ if\ AC-B^2<0\ and\ A>0\ or\ B>0$

 $F\left(x,y,z\right)=f\left(x,y,z\right)+\lambda g\left(x,y,z\right)$  

 $F\left(x,y,z\right)=f\left(x,y,z\right)-\lambda g\left(x,y,z\right)$  

 $F\left(x,y,z\right)=-f\left(x,y,z\right)+\lambda g\left(x,y,z\right)$  

 $\left(1,\ 2\right),\ \left(-1,\ 2\right)$  

 $\left(1,\ 2\right),\ \left(1,\ -2\right),\ \left(-1,\ 2\right),\ \left(-1,\ -2\right)$  

 $\left(1,\ 2\right),\ \left(-1,\ -2\right)$  

$f\left(x,\ y\right)=f\left(a,\ b\right)+\left[hf_x\left(a,\ b\right)+kf_y\left(a,\ b\right)\right]+\frac{1}{2!}\left[h^2f_{xx}\left(a,\ b\right)+2hkf_{xy}\left(a,\ b\right)+k^2f_{yy}\left(a,\ b\right)\right]$

$\left[h^2f_{xx}\left(a,\ b\right)+2hkf_{xy}\left(a,\ b\right)+k^2f_{yy}\left(a,\ b\right)\right]$

$f\left(x,\ y\right)=\left[hf_x\left(a,\ b\right)+kf_y\left(a,\ b\right)\right]+\frac{1}{2!}\left[h^2f_{xx}\left(a,\ b\right)+2hkf_{xy}\left(a,\ b\right)+k^2f_{yy}\left(a,\ b\right)\right]$

3

-2

-3