Question

hi
for any x>x0 , can we say that if f(x) <= g(x) then,
f'(x) < g'(x) ?

Answer 1

I doubt it.

Answer 2

What if f(x)=2 and g(x)=4, both have the same slope.

Answer 3

so what about if we say f'(x) < = g'(x)
I need it to solve something else
really need this
look
this is my explanation
if f < g
suppose it
and... lets suppose that
slope of f is greater than g
then
from one certain x to upper x
emmm....
f will croos g
and goes upper than g
right?
so...
if f always be smaller than g
so it has to has smaller slope

am i rught?

Answer 4

Not necessarily.

Answer 5

why?

Answer 6

If f = g, then f ' =g '

Answer 7

so

Answer 8

will it be true if i say ..... f' < = g' ?

Answer 9

i think it is true then

Answer 10

emmm... i think the functions must be countinuse... we need this condition

Answer 11

Not just continuous, but smooth, otherwise you can't find the derivative.

Answer 12

oh.... yes... thats sign of my confused mind... it is nessesery , thanks

Answer 13

I'm still not sure that it is true to say, "If f(x) ≤ g(x) then f '(x) ≤ g '(x) for all x."
I think f '(x) can locally be larger than g '(x) in some points, but overall f(x) will still be less than g(x).

Answer 14

f' is slope of f ,let me say my reasons in a better way...
down of g we have f
if slope of f = slope of g then they keep their distance for all x ... forever...
if slope of f < slope of g : their distance becomes more and more as x ---> large values
if slope of f > slope of g : their distannce become less until finally they meet anf then f goes upper than g which is counter of f<g .
so f ' < = g '

Answer 15

So you're saying that f ' is always greater than g ' at every point and not just at particular points?

Answer 16

not exactly i say for x > x0 .... from somewhere to... infinity

Answer 17

what u said cant happen because of countinuse condition of functions

Answer 18

What if f '(x) is less than g '(x) in some places, but is greater in others?

Answer 19

i think it cant happen, let me think and give a good reason

Answer 20

I could just draw a picture as an example.

Answer 21

ohhhhhhhhhhhhhhhhhhhhhhhh, u r right. i am sorry

Answer 22

yes i did too, u r right

Answer 23

U might be able to do it over a specified interval, that's about it, though...

Answer 24

Yep, you can state something similar, but you have to be careful about how you word the conditions.

Answer 25

emmm... right... thanks CliffSedge... u helped me...thank youuuuuuuuuuu others

Answer 26

i wanted to use this to prove something else , now i understood it is not true and have to find other way, u made i stop waisting time, thanks, later :)