How to graph f(x) if given f''(x)?

Question

anonymous · Answer

integrate it twice, will give you a whole family of curves.

anonymous · Answer

huh?

anonymous · Answer

$$\Large \int f''(x)dx=f'(x)+C  \
\Large \int\left(f'(x)+C\right)dx=f(x)+Cx+D$$

anonymous · Answer

I was looking for the graph

anonymous · Answer

Yes I understood that. Not sure how to make myself more clear,

how to graph f(x) <- apparently, if you integrate twice, then you have f(x), as you can see above. If you have f(x), then you need basic understanding of function plotting and you can graph it.

anonymous · Answer

If you're supposed not to do via integration, I understand, but in this case you need to share the graph you're given, because there is no straightforward method to compute the graph from f''(x) without integration, and as you can see above, also after integration you're left with constants that can take on various values within $\mathbb{R}$

stamp · Answer

@Itsamekid12 see attachment for visual explanation

anonymous · Answer

@stamp
Yes! Exactly! well done!