# Local maximum and global maximum.

• joejo
In summary, a local maximum is the highest point on a graph within a specific range, while a global maximum is the highest point for the entire range. To identify a local maximum, you must find the critical points and use the second derivative test. A local maximum can also be a global maximum, but this is not always the case. Local and global maxima are used in various real-world applications to optimize functions and find the best possible solution within a given range.
joejo
hey guys...Can someone help me out here...i'm trying to understand what the difference between a global maximum and a local maximum is? arn't they the same??

I'm not positive about this but I think that a local maximum is just the highest point in an area of the graph, not necessarily the highest point on the graph. The global maximum would be the highest point on the whole graph, no point would be higher than it is.

Sounds right to me.

thanks guys...can anyone explain in a bit detail so I can understand better

## 1. What is a local maximum?

A local maximum is a point on a graph where the function reaches its highest value within a specific range. This means that there may be other points on the graph with higher values, but they are not considered local maxima because they are outside of the specific range.

## 2. What is a global maximum?

A global maximum is the highest point on a graph for the entire range of the function. This means that there are no other points on the graph with higher values.

## 3. How do you identify a local maximum?

To identify a local maximum, you must first find the critical points of the function by finding where the derivative is equal to 0. Then, you can use the second derivative test to determine if the critical point is a local maximum or minimum. If the second derivative is negative, the point is a local maximum.

## 4. Can a local maximum also be a global maximum?

Yes, a local maximum can also be a global maximum if it is the highest point on the entire graph. However, this is not always the case as there may be other points on the graph with higher values outside of the specific range.

## 5. How are local and global maxima used in real-world applications?

Local and global maxima are used in various real-world applications in fields such as economics, engineering, and physics. It helps in optimizing functions and finding the best possible solution within a given range. For example, in economics, local and global maxima are used to determine the maximum profit for a company within a specific market range.

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