Alright, so now we're going to do a quick recap on how to find the maximum point on a graph and how to find the minimum point on a graph. So here in this example, I've got this kind of upside-down U, so how do we find the maximum or minimum point? So what you'll see is that not all graphs have a maximum or minimum. It's only when they kind of turn around like this, right, where they're going up, up, up, up, up, and then they turn around and start going down. Right? So when we want to find the maximum point, it's that point where it turns around. So if you notice here, the graph seems to be rising, rising, rising, rising, rising, rising, rising, and then on this side, it's falling, falling, falling. Right? So we've got to find that point where it turns around. So notice here it's still rising a little bit. Right? It's still rising a little bit, and then here it's pretty clear it's the point where it turns around. I'm going to do it in a different color there. So right here is the point where it turns around. We're not doing any math here. I just want to be able to identify the maximum and the minimum. So right here, that is our maximum. Okay? You're going to want to be able to do this, and find maximums and minimums on a graph. So what you'll notice is this one doesn't have a minimum. It went up up up to a point and then started going down down down. There wasn't a point where it was at a max bottom or max top. You might think this is a minimum here, this is a minimum here, but usually, these graphs are going to continue. So it would continue going down and it would be, you know, there wouldn't really be a minimum. So, in this case, when we see a critical point, it's kind of where it's turning around there, not where it just stops. Right? So that will be our critical point for our maximum, that we might want to identify. Let's do the same thing with a minimum point right here. So I'm thinking you guys can guess where the minimum point is going to be, but let's go ahead and do the same kind of method here. You see that the graph is falling and falling and falling, right, and then on the other side, it starts rising again. So there had to be a point where it turned around. It was falling for a while then now it's rising. Where did it turn around? It's right here. That is our minimum point, and for now all we want to do is be able to recognize when a graph has a minimum or a maximum, and then later on, we will be able to use this information when we're analyzing graphs. Cool? Alright. Let's move on.
Table of contents
- 0. Basic Principles of Economics1h 5m
- Introduction to Economics3m
- People Are Rational2m
- People Respond to Incentives1m
- Scarcity and Choice2m
- Marginal Analysis9m
- Allocative Efficiency, Productive Efficiency, and Equality7m
- Positive and Normative Analysis7m
- Microeconomics vs. Macroeconomics2m
- Factors of Production5m
- Circular Flow Diagram5m
- Graphing Review10m
- Percentage and Decimal Review4m
- Fractions Review2m
- 1. Reading and Understanding Graphs59m
- 2. Introductory Economic Models1h 10m
- 3. The Market Forces of Supply and Demand2h 26m
- Competitive Markets10m
- The Demand Curve13m
- Shifts in the Demand Curve24m
- Movement Along a Demand Curve5m
- The Supply Curve9m
- Shifts in the Supply Curve22m
- Movement Along a Supply Curve3m
- Market Equilibrium8m
- Using the Supply and Demand Curves to Find Equilibrium3m
- Effects of Surplus3m
- Effects of Shortage2m
- Supply and Demand: Quantitative Analysis40m
- 4. Elasticity2h 16m
- Percentage Change and Price Elasticity of Demand10m
- Elasticity and the Midpoint Method20m
- Price Elasticity of Demand on a Graph11m
- Determinants of Price Elasticity of Demand6m
- Total Revenue Test13m
- Total Revenue Along a Linear Demand Curve14m
- Income Elasticity of Demand23m
- Cross-Price Elasticity of Demand11m
- Price Elasticity of Supply12m
- Price Elasticity of Supply on a Graph3m
- Elasticity Summary9m
- 5. Consumer and Producer Surplus; Price Ceilings and Floors3h 45m
- Consumer Surplus and Willingness to Pay38m
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- Economic Surplus and Efficiency18m
- Quantitative Analysis of Consumer and Producer Surplus at Equilibrium28m
- Price Ceilings, Price Floors, and Black Markets38m
- Quantitative Analysis of Price Ceilings and Price Floors: Finding Points20m
- Quantitative Analysis of Price Ceilings and Price Floors: Finding Areas54m
- 6. Introduction to Taxes and Subsidies1h 46m
- 7. Externalities1h 12m
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- 10. The Costs of Production2h 35m
- 11. Perfect Competition2h 23m
- Introduction to the Four Market Models2m
- Characteristics of Perfect Competition6m
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- Perfect Competition Profit on the Graph20m
- Short Run Shutdown Decision33m
- Long Run Entry and Exit Decision18m
- Individual Supply Curve in the Short Run and Long Run6m
- Market Supply Curve in the Short Run and Long Run9m
- Long Run Equilibrium12m
- Perfect Competition and Efficiency15m
- Four Market Model Summary: Perfect Competition5m
- 12. Monopoly2h 13m
- Characteristics of Monopoly21m
- Monopoly Revenue12m
- Monopoly Profit on the Graph16m
- Monopoly Efficiency and Deadweight Loss20m
- Price Discrimination22m
- Antitrust Laws and Government Regulation of Monopolies11m
- Mergers and the Herfindahl-Hirschman Index (HHI)17m
- Four Firm Concentration Ratio6m
- Four Market Model Summary: Monopoly4m
- 13. Monopolistic Competition1h 9m
- 14. Oligopoly1h 26m
- 15. Markets for the Factors of Production1h 33m
- The Production Function and Marginal Revenue Product16m
- Demand for Labor in Perfect Competition7m
- Shifts in Labor Demand13m
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- Differences in Wages6m
- Discrimination6m
- Other Factors of Production: Land and Capital5m
- Unions6m
- Monopsony11m
- Bilateral Monopoly5m
- 16. Income Inequality and Poverty35m
- 17. Asymmetric Information, Voting, and Public Choice39m
- 18. Consumer Choice and Behavioral Economics1h 16m
1. Reading and Understanding Graphs
Finding the Maximum and Minimum Points on Graphs
1. Reading and Understanding Graphs
Finding the Maximum and Minimum Points on Graphs - Online Tutor, Practice Problems & Exam Prep
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To identify maximum and minimum points on a graph, look for critical points where the graph changes direction. A maximum occurs at the peak, where the graph rises and then falls, while a minimum is at the lowest point, where it falls and then rises. Not all graphs have both; some may only have a maximum or none at all. Recognizing these points is essential for analyzing graphs effectively, as they indicate significant changes in the behavior of the function represented.
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Finding Maximum and Minimum on a Graph
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