Does the antiderivative of a function gives any information about it's graph?

This question may look a little obvious but here we go:

In every Calculus 1 course we learn that using a function's firth and second derivatives we can know a lot of things about it's graph.

But if we only have an antiderivative of a function( for example) can we know anything about it's graph before differentiating?

I guess that could it be something like , since the classic Galileo equation for uniform acceleration .

Thanks for answering (Wink)

Re: Does the antiderivative of a function gives any information about it's graph?

I presume that you have learned that the anti-derivative (integral) gives the area under the curve.