Finding Absolute Maximum and Minimum Values - Absolute Extrema

TL;DR

Learn how to identify the highest and lowest points on a graph, as well as local maximum and minimum points, using Y values and slope.

Transcript

in this lesson we're going to focus on identifying the location of the absolute maximums and minimums of a function so let's start with a graph so you can visually see it and let's say if we have a function that looks like this so let's call this point a point B C and D identify the location of any absolute and relative extrema of this particular g... Read More

Key Insights

• 😥 Absolute maximum is the highest point on a graph, while the absolute minimum is the lowest point.
• 😥 Local maximum and minimum points are the highest and lowest points in specific local areas.
• 📌 Relative extrema are identified by finding locations where the slope is 0 using the first derivative.
• 😀 To find absolute and relative extrema, compare the y-values of the function.
• 😥 The slope of the function determines whether a point is a relative minimum or maximum.
• #️⃣ Endpoints of the interval and critical numbers are important in identifying absolute extrema.
• 😀 The y-values of the function determine the absolute maximum and minimum values.

Questions & Answers

Q: What is the difference between absolute maximum and relative maximum?

The absolute maximum is the highest point on the entire graph, while the relative maximum is the highest point in a specific local area.

Q: How do you identify relative extrema?

To identify relative extrema, you need to find locations where the slope is 0 by using the first derivative of the function.

Q: How can you determine if a point is a relative minimum or maximum?

By analyzing the slope of the function. If the slope changes from negative to positive across the critical point, it is a relative minimum. If the slope changes from positive to negative, it is a relative maximum.

Q: How do you find the absolute maximum and minimum values?

Make a data table with the endpoints of the interval and any critical numbers. Plug in the x-values into the function to determine the corresponding y-values. The highest y-value is the absolute maximum, and the lowest y-value is the absolute minimum.

Summary & Key Takeaways

• Absolute maximum is the highest point on a graph, while absolute minimum is the lowest point.

• Local maximum is the highest point in a local area, and local minimum is the lowest point in a local area.

• To identify absolute extrema, compare Y values. To identify relative extrema, find locations where the slope is 0.