If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Class 11 Physics (India)

### Course: Class 11 Physics (India)>Unit 3

Lesson 10: Maximum and minimum points

# Worked example: absolute and relative extrema

Extrema is the general name for maximum and minimum points. This video shows how to identify relative and absolute extrema in the graph of a function.

## Want to join the conversation?

• At 1.37 Sal said that the specified point is not a relative maximum. According to the definition for a relative maximum:
f(a) is rel. maxima when all the x near it are f(a) <= f(x)

In the example, the specified point lies at a position, where the points left of it are all equal to it and the points right of it are less than it. Therefore, doesn't that make the specified point a rel. maxima?
• I had just watched the previous video and I thought the same. If it was for me to do, I would call this a relative maximum point
• Wait a minute, but what if the map shows a function that has two points that are the same height, but says plot the absolute maximum?
• That scenario shouldn't happen. There will be one absolute max or min if they ask you to mark it (it can happen in a function, you just won't get it as a question since in that case there isn't an absolute max/min).
• What is the difference between absolute maximum and global maximum?
• At , Sal says that the point (3,-8) would be a relative maximum point but how is that possible? The function is only till -8. How can we assume that the function will have the greatest value considering the points around it? I hope I made my question clear.
• Sal told us at the beginning of the video that the domain was closed, that is, it included the end points. The domain is [-8,6]. On this particular graph, if we start at x=-8, and move towards the right on the x axis, the next immediate f(x) is less than it was at x=-8. Because we are on a closed interval, that makes the point (-8, 3) a relative maximum. (Make sure you put your x coordinate first when referring to a point on a graph😊.)
• So what is the difference between absolute max/min point and global max/min point?
• They're the same. Maybe you mean relative max/min point and global/absolute max/min point.
A relative max/min point is a point higher or lower than the points on both of its sides while a global max/min point is a point that is highest or lowest point in the graph. In other words, there can be multiple relative max/min points while there can only be one global/absolute max/min point.
• Is it possible for a function to have multiple global minima? For example, a sin or cos wave has similar value in their minimum/maximum. How those minima and maxima should be called? Do sin wave and cos wave have global minima or do they have only local minima?
• By definition of absolute/global minimum and maximum you cannot have multiple of these points. You can have multiple points that are the absolute/global min or max though there would still be only 1 absolute/global min or max.

For example, on the last graph that Sal uses the absolute/global max point is 7. We can have another point on the graph that is 7, but that doesn't mean we have multiple absolute/global max it just means that there are 2 points with the absolute/global max. If another point was created on that was y=8 then 7 would no longer be the absolute/global max because 8 would be the absolute/global max.

There might be some terminology for this, but I don't know what it is.
(1 vote)
• Just making sure, there can be more than one relative minimum or maximum point?
• Yes, there can exist more than one relative minimums and relative maximums.