graphs of f'(x) and f(x)

[learmijo]

How do you determine how the graph f(x) looks like when you know what f'(x) graph looks like. (vice versa) :?

 

[stapel]

Since you lose any constant terms upon differentiation, you cannot "find" the graph of f(x) from f'(x). You might get kind of close, but you'd have to allow for an unknown vertical shift. (And you'd have to allow for a certain amount of guessing, since you're working from a picture rather than exact algebra.)

If you have the graph of f(x), then look at the slope at each point (well, roundsabout each region, I guess), and draw that value for the corresponding f'-value.

Eliz.

 

[tkhunny]

One would think about how they relate to each other and draw appropriate conclusions.