Question

If f'(x)=g'(x) for all x in an interval I, what is the relationship between f and g

Answer 1

hmm let me give u idea, it says f'(x) = g'(x) in an interval and deriviate is anti integral,... then there should be limits a,b hmmmm... never faced with a question like that :D but i think we can se if we do integral with limits (a,b) (f'(x)).. let me write \[\int\limits_{a}^{b}f'(x) = \int\limits_{a}^{b}g'(x) \]

Answer 2

i don't know if my idea is true :D

Answer 3

both functions are continuous along the interval but dont get confused with equal, they differ by a constant somehow.....example f(x)=x^2+5 and g(x)=x^2 then f'(x)=2x and g'(x)=2x

Answer 4

well i think johnny and i said the same thing :D

Answer 5

haha yeah true

Answer 6

i <3 integral

Answer 7

but shortie u got it?

Answer 8

Okay so they are the same with different constants?

Answer 9

If you were to draw the graphs of f(x) and g(x) on the same axis, you would probably end up with two copies of the same graphs, with an arbitrary vertical distance between each other. Or else you would end up drawing only one graph if it happens that both graphs have the same constant.

Answer 10

well they are not same funcs they are different from each other but somehow, their derivatives gives the same result in an interval so that you can say \[\int\limits_{a}^{b}f'(x) = \int\limits_{a}^{b}g'(x)\]

that eans f(x) = g(x) from for the x values from a to b :D but if the x value won't be between a and b then the result won't be f(x) = g(x) and fucns give different result, the results are only same in an invidial not at all so that the funs are not same okay?

Answer 11

f(x)=g(x)+c on I