Question

Find an equation of the plane tangent to the surface e^(xy) + z^2 – z = 1 at the point (0, -1, 1).

Answer 1

the tangent plane has a remarkable similarity to the point slope form of a line

Answer 2

i think of it as the point slop slope form of a plane

Answer 3

\[z-z_o=Fx(x-x_o)+Fy(y-y_o)\]

Answer 4

or, another way to view it, is:\[Fx(x-x_o)+Fy(y-y_o)+Fz(z-z_o)=0\]

Answer 5

F(x,y,z) = e^(xy) + z^2 – z = 1

Fx(x,y,z) = ye^(xy)

Fy(x,y,z) = xe^(xy)

Fz(x,y,z) = 2z – 1

apply your point to those to define them