Tangent Planes

Let $f: \mathbb{R}^2 \to \mathbb{R}$. Tangent plane at a point $P(a,b)$ is given by:

To a Level Surface

Let

• $F(x,y,z)$ is a 3-variable function
• $S$ is the level surface of $F$ at $F(x,y,z)=k$
• $P = (x_0,y_0,z_0)$ be a point on $S$

The equation of the tangent plane on $P$ at the surface $S$: