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.