Sketching Antiderivatives: Tips and Links for Quick Refresh

[swears]

Wow, I totally forgot how to do these.

I have a graph of a line, but it does not say the function. I have to sketch the antiderivative.

Does anyone have any links or advice to start me out.

TIA

 

[berkeman]

Remember that the derivative dy/dx is the change in the y value per change in the x value. So the derivitave at a point is basically the slope of the line.

Now turn that reasoning around to figure out the antiderivative. If you have a plot of the slope of the line at all points, then you can figure out what the original function's line looked like. Quiz question -- what other thing do you have to add into the final antiderivative answer to make it correct?

 

[berkeman]

And here's a link to wikipedia's antiderivative entry:

http://en.wikipedia.org/wiki/Antiderivative

 

[swears]

Yeah, I can do the derivative if I see the graph. I just can't visualize that backwards in my head.

These are the values I'm dealing with: f'(x)| 0 | 1 | 0 | -1 | 0
............x |-1 | 0 | 1 | 2 | 3

 

[stefannm]

What kind of function is the integral of a line? A parabola right. Well, were is the vertex of that parabola? You should think about what a critical point is. Maybe the first derivative test. Does any of this help?

 

[swears]

It is going up until x=0, then goes down. It is concave down there.

The at x = 1 it change to concave up and at x = 2 it starts increasing.

So, I guess the critical points are x = 0, 1, 2

 

[stefannm]

A critical point is where f'(x) = 0. If I am reading your notation right, then the critical points are x = -1, 1, 3. So if there are 3 critical points, then the [EDIT]antiderivative should be a function of x^4. What does this kind of function look like?

 

[swears]

Well actually, f'(x) is only 0 at x= 0 and 2, but it switches concavity at 1, so I figured that would be one too. (guess not)

x^4, yeah I believe so, I don't have a calculator to confirm(working on it), but it has two parabolas in it.(1 upside down).

 

[stefannm]

Oh, Sorry, I had some trouble reading your points. Sounds like you are on the right track though.