Stuck with finding function from graph of its derivative.

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Homework Help Overview

The discussion revolves around understanding how to derive a function from the graph of its derivative. The original poster describes a piecewise linear function defined over the interval [-2, 5], with specific slopes given for different segments based on the derivative.

Discussion Character

  • Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to interpret the relationship between the derivative and the original function, expressing confusion about how to graph the function based on the provided derivative information. Some participants clarify that the derivative represents the slope of the original function at specific points, while others question the terminology used by the original poster.

Discussion Status

The discussion is ongoing, with some participants providing clarifications about the nature of derivatives and their relationship to the original function. There is a sense of progress as the original poster acknowledges understanding after receiving feedback.

Contextual Notes

The original poster mentions restrictions on using integration, indicating a focus on conceptual understanding rather than computational methods. There is also a reference to missing class material, which may contribute to the confusion experienced.

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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