Stuck with finding function from graph of its derivative.

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SUMMARY

The discussion focuses on graphing a function f based on its derivative, which is provided as a step function over the interval [-2, 5]. The derivative values are specified as y' = -2 for x in [-2, 0), y' = 0 for x in (0, 1), y' = 1 for x in (1, 3), and y' = -1 for x in (3, 5]. The participant expresses confusion about how to graph the function without using integration, emphasizing the need to understand the relationship between the derivative and the slope of the original function. The conclusion drawn is that the derivative indicates the slope of the function at any given point.

PREREQUISITES
  • Understanding of basic graphing techniques
  • Knowledge of derivatives and their interpretation as slopes
  • Familiarity with step functions
  • Ability to analyze closed intervals in mathematics
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  • Study the concept of piecewise functions and how to graph them
  • Learn about the Fundamental Theorem of Calculus for future integration applications
  • Explore graphical representations of derivatives and their corresponding functions
  • Practice problems involving the interpretation of slopes from derivative graphs
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Students in calculus, particularly those struggling with the concepts of derivatives and graphing functions, as well as educators seeking to clarify these topics for their students.

devilazy
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So the question asks me to use the following information to graph the function f over the closed interval [-2, 5]
i) The graph of f is made of closed line segments joined end to end.
ii) The graph starts at the point (-2, 3)
ii) The derivative of f is the step function in the figure shown here.
That's all give as well as a graph, but I don't know how to put a graph on so I'll just state it's points.
x: [-2 to 0) y' = -2
x: (0 to 1) y' = 0
x: (1 to 3) y' = 1
x: (3 to 5] y' = -1

I am totally clueless of what to do, I missed that class and wasn't able to catch up to what I missed. I tried reading through the text to see if it says anything about this but found nothing. I know y' is basically the slope of f(x), and I know how to do integration (but I am not allowed to use it, as we haven't gotten there yet). Anyways, my point is I tried integrating the y' but yea, it just makes no sense to me. I hate graphs.
I would love any idea, I just wish to understand how to do this and then I'll be fine figuring out the rest.
 
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The derivative of a function at a point is just the slope of the function at that point. Does that help?
 
Yea i figured that out, so that mean the line of the derivative is just the slope of the original graph?
 
I don't know what that question means. What is the line of the derivative?

The value of the derivative at a point is the slope of the original function at that point.

For example.

If y' = 2 then the slope of y at x is 2.
 
Ah, I got it. Thanks a lot.
 

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