Tangent plane quiz {cal3, exm2}

Quiz!

• $f(x,y)=e^{-x^2-y^2}$

• Find plane tangent to $f(x,y{)}_x$

• Find the direction of greatest ascent of given tangent plane

• Let $c=-x^2-y^2$

• We find $f_x(x,y)=-2x{e}^c$, $f_y(x,y)=-2y{e}^c$

• Turn $f_x=S_x(s,t)\to <s,t,-2s{e}^{-s^2-t^2}>$

• We then take partials of s and t

• Take cross product of both first partials, some $n$