Exploring Graphs of y, y', and y'' in Relation to Anti-Derivatives

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In summary, a graph is a visual representation of data that uses points, lines, and bars to show the relationship between variables. The type of graph used depends on the type of data and the purpose of the analysis. The key elements of a graph include the title, axis labels, legend, data points, and scale. To interpret a graph, one should identify the type and variables, analyze trends and compare values, and read accompanying information. Graphs can be created using software or online tools by inputting data, selecting the graph type, and customizing it with titles, labels, and scale adjustments.
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Miike012
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Homework Statement



Say y = x^3

Then: y' = 3x^2
y'' = 6x


My question is... Let's say I graphed y y' and y''. Do these graphs give us any info about the anti derived graph?

For instance just by looking at the y' graph can I gather up any info for y graph?
 
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  • #2
Yep. Where y' is 0, the slope is zero and the graph has a critical point. Where y'>0, you know the graph is going up. Where y'<0, you know the graph is going down.

This is all covered in curve sketching.
 

FAQ: Exploring Graphs of y, y', and y'' in Relation to Anti-Derivatives

What is a graph?

A graph is a visual representation of data that uses points, lines, and bars to show the relationship between different variables. It is a useful tool for analyzing and interpreting data.

How do you choose the type of graph to use?

The type of graph used depends on the type of data and the purpose of the analysis. Line graphs are best for showing trends over time, bar graphs are useful for comparing data from different categories, and pie charts are helpful for displaying proportions.

What are the key elements of a graph?

The key elements of a graph include the title, axis labels, legend, data points, and scale. These elements help to clearly communicate the information being presented and make the graph easy to understand.

How do you interpret a graph?

To interpret a graph, you should first identify the type of graph and the variables being shown. Then, look at the trend or pattern of the data, and compare the values between different data points. It is also important to read the axis labels and any accompanying information to fully understand the graph.

How do you create a graph?

To create a graph, you can use a variety of software or online tools, such as Microsoft Excel or Google Sheets. First, input your data into a spreadsheet and then select the appropriate graph type. Customize the graph by adding titles, labels, and adjusting the scale to accurately represent the data.

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