Drawing f(x), f'(x) and f"(x) (1 Viewer)

[passion89]

I've just come across a few harder questions that are asking me to draw f(x) after showing me what f'(x) and f"(x) look like. (There are no values)

How do you know what the graph is supposed to look like when there are no values/equations?

Are there any particular steps that need to be taken when drawing the different derivatives?

 

[Riviet]

Some pointers:

* X-intercepts of f'(x) will be stationary points on f(x).

* Wherever f'(x)>0, f(x) will have positive gradient and for f'(x)<0, f(x) will have negative gradient.

* X-intercepts of f''(x) will be points on f(x) where the concavity on f(x) changes.

* Wherever f''(x)>0, f(x) will be concave up; whenever f''(x)<0, f(x) will be concave down.

* X and y intercepts on f(x) are indeterminable unless given specific information in the question.

Anyone else feel free to add to my list.

 

[passion89]

That's exactly what I needed, thank you!

 

[pLuvia]

Also to add:
Point of inflexions on f(x) will become stationary points on the f'(x) curve