Answer to Question #52107 in Calculus for john

Question

1)Find the directional derivative of f(x,y,z)=xy^(2)-z^(2)in the direction of v=(1,-2,2) at (2,1,3)
2)Suppose f(1,0,0)=-3,fx(1,0,0)=-2,fy(1,0,0)=4 and fz(1,0,0)=2 . Use linear approximation to estimate f(1.02,0.01,-0.03).
3)Find an equation of the tangent plane at the point(4,1) of the surface z=x^(2)+y^(-2)