Thread: Please check if I drew graph correctly?

I wrote it by hand and this is just a rough sketch, but I'm just wondering if I got the general shape correct?

The only place I think I might have went wrong is "lim y x-> -2 does not exist".

Any help would be greatly appreciated

What does "f(0), f(3) = 0, f''(1) 0" mean?

Since f'(x) < 0 for x < -2 and -2 < x < 0, the function is monotonic on those intervals and therefore has limits from the left and from the right at -2. Since there is no overall limit, the one-sided limits must be different.

Also, you need to make sure the function is concave/convex on the required intervals.

I appreciate the quick response; maybe you're Russian, if so, огромное спасибо)

Originally Posted by emakarov

What does "f(0), f(3) = 0 mean

I believe it means that either a local maximum or local minumum occurs at one of those points?

Originally Posted by emakarov

f''(1) 0" mean?

I believe it means that the point of inflexion is 1.

Originally Posted by emakarov

Since f'(x) < 0 for x < -2 and -2 < x < 0, the function is monotonic on those intervals and therefore has limits from the left and from the right at -2. Since there is no overall limit, the one-sided limits must be different.

This is the part I don't get well. The function is monotonic, but not continous, thus the shape must be the same with a small disconnect, no?

Originally Posted by emakarov

Also, you need to make sure the function is concave/convex on the required intervals.

I also wasn't sure about this. It says "intervals", as such, does that mean it can simply "begin" being concave or convex or does it have to be completely concave/convex in those intervals? What do you think?

Originally Posted by Goll

I appreciate the quick response; maybe you're Russian, if so, огромное спасибо)

Пожалуйста.

Originally Posted by emakarov

What does "f(0), f(3) = 0 mean

Originally Posted by Goll

I believe it means that either a local maximum or local minumum occurs at one of those points?

In this case it should say "f '(0) = f '(3) = 0".

Originally Posted by emakarov

f''(1) 0" mean?

Originally Posted by Goll

I believe it means that the point of inflexion is 1.

In this case it should say "f ''(1) = 0".

Originally Posted by Goll

This is the part I don't get well. The function is monotonic, but not continous, thus the shape must be the same with a small disconnect, no?

Yes, though the phrase "the shape must be the same with a small disconnect" is not precise. See Wikipedia.

Originally Posted by Goll

I also wasn't sure about this. It says "intervals", as such, does that mean it can simply "begin" being concave or convex or does it have to be completely concave/convex in those intervals?

You just need to make sure that the second derivative is as required. In your picture, (I understand that it's a sketch), the graph seems to be composed of straight lines whose second derivative is zero.