Paul's Online Math Notes
Online Notes / Calculus III (Notes) / Applications of Partial Derivatives
I've been notified that Lamar University will be doing some network maintenance on August 9 during the hours of 8:00 AM through Midnight Central Daylight Time. During this time the site will either be completely unavailable or you will receive an error when trying to access any of the notes and/or problem pages. I realize this is probably a bad time for many of you but I have no control over this kind of thing and there are really no good times for this to happen and they picked the time that would cause the least disruptions for the fewest people. I apologize for the inconvenience!


Internet Explorer 10 & 11 Users : If you are using Internet Explorer 10 or Internet Explorer 11 then, in all likelihood, the equations on the pages are all shifted downward. To fix this you need to put your browser in Compatibility View for my site. Click here for instructions on how to do that. Alternatively, you can also view the pages in Chrome or Firefox as they should display properly in the latest versions of those browsers without any additional steps on your part.

In this section we will take a look at a couple of applications of partial derivatives.  Most of the applications will be extensions to applications to ordinary derivatives that we saw back in Calculus I.  For instance, we will be looking at finding the absolute and relative extrema of a function and we will also be looking at optimization.  Both (all three?) of these subjects were major applications back in Calculus I.  They will, however, be a little more work here because we now have more than one variable.


Here is a list of the topics in this chapter.


Tangent Planes and Linear Approximations  We’ll take a look at tangent planes to surfaces in this section as well as an application of tangent planes.


Gradient Vector, Tangent Planes and Normal Lines  In this section we’ll see how the gradient vector can be used to find tangent planes and normal lines to a surface.


Relative Minimums and Maximums  Here we will see how to identify relative minimums and maximums.


Absolute Minimums and Maximums  We will find absolute minimums and maximums of a function over a given region.


Lagrange Multipliers  In this section we’ll see how to use Lagrange Multipliers to find the absolute extrema for a function subject to a given constraint.

Online Notes / Calculus III (Notes) / Applications of Partial Derivatives

[Contact Me] [Links] [Privacy Statement] [Site Map] [Terms of Use] [Menus by Milonic]

© 2003 - 2014 Paul Dawkins