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.