Stuck with finding function from graph of its derivative.

In summary, the function f is graphed over the closed interval [-2, 5] using closed line segments joined end to end. The graph starts at the point (-2, 3) and the derivative of f is a step function with slopes of -2, 0, 1, and -1 at different intervals. The derivative at a point is the slope of the original function at that point.
  • #1
devilazy
15
0
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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  • #2
The derivative of a function at a point is just the slope of the function at that point. Does that help?
 
  • #3
Yea i figured that out, so that mean the line of the derivative is just the slope of the original graph?
 
  • #4
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.
 
  • #5
Ah, I got it. Thanks a lot.
 

FAQ: Stuck with finding function from graph of its derivative.

How do I find the function from the graph of its derivative?

The process of finding the function from the graph of its derivative involves integration. First, you need to identify the points of inflection on the derivative graph, which will correspond to the maximum or minimum points on the original function. Then, you can use integration techniques to find the original function. Keep in mind that there may be multiple functions that have the same derivative, so you may need additional information to determine the exact function.

What information do I need to find the function from its derivative graph?

In addition to the points of inflection, you will need to know the slope of the original function at a specific point in order to find the function. This can be obtained by finding the slope of the tangent line at that point on the derivative graph.

Is it possible to find the function from its derivative graph without integration?

No, integration is a necessary step in finding the function from its derivative graph. This is because the derivative only gives information about the rate of change of the function, not the actual values of the function.

Can I use a computer or calculator to find the function from its derivative graph?

Yes, there are computer programs and calculators that can perform numerical integration to find the function from its derivative graph. However, it is important to note that these methods may not always be accurate and may not work for more complex functions.

Are there any shortcuts or tricks for finding the function from its derivative graph?

There are some shortcuts and tricks that can help in finding the function from its derivative graph, such as using symmetry or known properties of common functions. However, these methods may not always be applicable and integration is still the most reliable way to find the function.

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