Lesson 24 – Maxima and Minima of Functions of Several Variables
1
Lesson 24
Maxima and Minima of Functions of Several Variables
We learned to find the maxima and minima of a function of a single variable earlier in the course.
Although we did not use it much, we had a second derivative test to determine whether a critical
point of a function of a single variable generated a maximum or a minimum, or possibly that the test
was not conclusive at that point.
We will use a similar technique to find relative extrema of a
function of several variables.
Since the graphs of these functions are more complicated, determining relative extrema is also more
complicated.
At a specific critical number, we can have a max, a min, or something else.
That
“something else” is called a saddle point.
The method for finding relative extrema is very similar to what you did earlier in the course.
First, find the first partial derivatives and set them equal to zero.
You will have a system of
equations in two variables which you will need to solve to find the critical points.
Second, you will apply the second derivative test. To do this, you must find the secondorder
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 Fall '08
 CONSTANTE
 Critical Point, Derivative

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