Tangent Planes

Definition

Notes

Intersection of 2 planes is a straight line.

Partial derivative with respect to x and y are constant values regardless of values of x and y. $\frac{\partial L}{\partial x}$ $\frac{\partial L}{\partial y}$

Methods

Find Tangent Plane

Given function $f:\to (x,y)$ and point x $(x\_0,y\_0)$ determine the tangent plane at that point.

The formula is:

$$L(x,y)=a(x-x\_0)+b(y-y\_0)+k$$

Where a is $\frac{\partial L}{\partial y}$ the partial derivative of the function with repsect to x. In other words the slope of x at point $x\_0$.

b is $\frac{\partial L}{\partial x}$ b is the partial derivative of L with respect to y at $y\_0$. This is also the slope of y at this point.