Graphing Increase/Decrease Intervals of a Function

In summary, when finding the intervals of increase/decrease in a function, there are several steps that need to be taken before graphing. These steps may include creating a table of signs for the first derivative and other methods. If unsure, it is best to start with the most basic way of graphing a function.
  • #1
calc
5
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once you find the intervals of Increase/Decrease in a function how do u graph that??
 
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  • #2
calc said:
once you find the intervals of Increase/Decrease in a function how do u graph that??

What do u mean??There are several steps to be taken before graphing a function.The tabel of signs for the first derivative is just one of them...Between that and the graphing,there are more steps to be taken...

Please,give a spacific example...And I'm willing to show what to do in order to graph the function...

Daniel.
 
  • #3
I don't mean to be rough on you have asked to questions in which you have said you knew how to find intervals of increase/decease, maxima and minima, inflection points, etc. but don't know how to graph a function. Are you clear on what a "graph" is. For example, if you were given a function you had never seen before and couldn't calculate derivatives or anything like that, how would you graph it? What is the most basic way to graph a function?
 

FAQ: Graphing Increase/Decrease Intervals of a Function

1. What is the purpose of graphing increase/decrease intervals of a function?

The purpose of graphing increase/decrease intervals of a function is to visually represent the changing behavior of a function over a specific interval. It allows us to see where the function is increasing, decreasing, or staying constant, which can help us understand the overall behavior of the function.

2. How do you determine the increase/decrease intervals of a function from its graph?

To determine the increase/decrease intervals of a function from its graph, you can look for areas where the graph is sloping upwards (increasing) or downwards (decreasing). You can also look for any horizontal segments, which indicate a constant interval. By identifying these intervals, you can determine the overall trend of the function.

3. What is the significance of the slope of a function in determining its increase/decrease intervals?

The slope of a function is directly related to its increase/decrease intervals. A positive slope indicates an increasing interval, while a negative slope indicates a decreasing interval. A slope of zero represents a constant interval. By analyzing the slope of a function, we can determine its increase/decrease intervals and better understand its behavior.

4. Can a function have both increasing and decreasing intervals?

Yes, a function can have both increasing and decreasing intervals. This occurs when the function has alternating intervals of increase and decrease. For example, a function may increase for a certain interval, then decrease for another interval, and then increase again. This behavior can be seen by analyzing the slope of the function's graph.

5. How can graphing increase/decrease intervals of a function help in real-world applications?

Graphing increase/decrease intervals of a function can be useful in real-world applications such as analyzing stock market trends or predicting population growth. By understanding the behavior of a function, we can make informed decisions and predictions about future outcomes. In addition, graphing can help us visually communicate complex data and make it easier to interpret and understand.

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