HW#II

$(1)$ Given that the directicu of derivative of $f(x,y,z)$ at the point $(3,-2,1)$ in the direction of vec$(v)=2i-j-2k$ is $-5$ and $||vec(grad)f(3,2,1)||=5,$ find vec$(grad)f(3,-2,1).$

$(2)$ Find all points on the surface $2x^2+3y^2+4z^2=9$ at which the tangent plane is parallel to the plane $x-2y+3z=5$

$(3)$ Find all relative extrewa and saddle point of $f(x,y)=e^{-(x^2+y^2+2x)}.$