4.7 Maximum and Minimum Values
, Maximum and Minimum Values
In this section we see how to use partial derivatives to
locate maxima and minima of functions of two variables.
Look at the hills and valleys in the graph of f shown in
Figure 1.
Figure 1
2
, Maximum and Minimum Values
There are two points (a, b) where f has a local maximum,
that is, where f (a, b) is larger than nearby values of f (x, y).
The larger of these two values is the absolute maximum.
Likewise, f has two local minima, where f (a, b) is smaller
than nearby values.
The smaller of these two values is the absolute minimum.
3
, Maximum and Minimum Values
If the inequalities in Definition 1 hold for all points (x, y)
in the domain of f, then f has an absolute maximum
(or absolute minimum) at (a, b).
4
, Maximum and Minimum Values
In this section we see how to use partial derivatives to
locate maxima and minima of functions of two variables.
Look at the hills and valleys in the graph of f shown in
Figure 1.
Figure 1
2
, Maximum and Minimum Values
There are two points (a, b) where f has a local maximum,
that is, where f (a, b) is larger than nearby values of f (x, y).
The larger of these two values is the absolute maximum.
Likewise, f has two local minima, where f (a, b) is smaller
than nearby values.
The smaller of these two values is the absolute minimum.
3
, Maximum and Minimum Values
If the inequalities in Definition 1 hold for all points (x, y)
in the domain of f, then f has an absolute maximum
(or absolute minimum) at (a, b).
4
