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Find an equation for and sketch the graph of the level curve of the function $f(x, y)$ that passes through the given point.$$f(x, y)=16-x^{2}-y^{2}, \quad(2 \sqrt{2}, \sqrt{2})$$

$$\begin{array}{c}6=16-x^{2}-y^{2} \\x^{2}+y^{2}=10\end{array}$$

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

Campbell University

Oregon State University

Harvey Mudd College

University of Nottingham

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

01:42

Find an equation for, and …

01:07

Find an equation for and s…

01:53

02:18

Find an equation and sketc…

02:24

Sketch the graph of the fu…

01:16

Sketch the graph of $f$

02:36

01:52

01:30

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