Partial Derivatives

Reading

Sections 15.4

Problems

• Practice Problems 15.4: 3, 5, 11, 13, 15, 17, 18, 25, 27
• Problems to turn in 15.4: 6, 12, 14, 16, 26

Topics to know

1. Linearization for functions of two variables, tangent plane. Why is there only one plane equation that makes sense?
2. Definition of a function being differentiable at a point.
3. Example of \(f(x, y) = L(x, y) + e(x, y)\) decomposition for \(f(x,y) = x^2 + 2x - xy\) at \((0, 0)\). Also try another point, e.g. \((1, 2)\)
4. \(f\) is differentiable if both \(f_x\) and \(f_y\) exist and are continuous in a disc around the point of interest.
5. Various ways of writing the linear approximation.
6. Find point on which tangent plane is parallel to a given plane.