f' (x) = g' (x); What's the relationsip of f(x) an g(x)?

[Miyengar]

If f'(x) = g'(x) for all X, we know that f(x) need not egual g(x) for all values of x, right?

What's the relationship between f(x) and g(x)?

How do we prove this relationship?

Thanks!

 

[Matt]

They differ by at most a constant.

From the fact that f'(x)=g'(x) for all x, you know that (f-g)'(x)=0 for all x. Integrate both sides of this equation to obtain the desired result.

 

[Miyengar]

Thanks! Stupid question, but how do you integrate both sides?

Thanks, again