Consider the field . The surface we have is .
The normal at any point is .
In this case it is .
Is that your question?
find the eqn of the tangent plane to the surface
z=f(x,y)=x^2 +4y^2
at the point (a,b,a^2 +4y^2)
What I don't understand is how the normal to the plane at point a,b is geven by:
n=(fx,fy,-1)
would fx not be the "rate of change with respect to x" and not the NORMAL to the plane at that point?
maybe i am confused about fx, fy and fz.
I always thought it was the rate of change with respect to x and thus being the tangent to a surface?
The normal is perpendicular to the surface correct?
I have some fallacy in my understanding. Any clarification?