Can f(x) ever be greater than e^x?

[shgidi]

we have f(0)=1, f '(x)>=f(x)

we shall prove f(x)>e^x for every x>=0

thanx to the solvers

 

[ice109]

what? that's not true f(0) = e^0

 

[shgidi]

sorry, i had a smal mistake:

we have f(0)=1, f '(x)>=f(x)

we shall prove f(x)>=e^x for every x>=0

thanx to the solvers

 

[Gib Z]

Ok. Welcome to Physicsforums shgidi, I hope you enjoy it here =]

Please read our homework policy (theres a sticky at the top of this sections page), you must post your homework in the homework section! Also, we require you must show us any work that you have attempted (and yes you must attempt whatever you know) because otherwise its not helping you, its just doing your homework!

It is only because I am so VERY nice that I will give you a hint :P
In the interval we are interested in, x \geq 0, the function is always increasing because f(0) = 1, so f'(0) is great than 1, and they both just keep increasing. Since they are both positive, divide by f(x) on both sides. Now take an integral of that inequality from 0 to t. I basically did it for you :(

 

[shgidi]

OK, I promise for the next time to look and find the homework section.
I've posted my question here, because I saw here many questions in the same style, so I thought it would fit.

anyway, 10x for your solution, but it doesn't quiet help me, because Integrals is not part of the material of my current course.

 

[HallsofIvy]

OK, I promise for the next time to look and find the homework section.
I've posted my question here, because I saw here many questions in the same style, so I thought it would fit.

anyway, 10x for your solution, but it doesn't quiet help me, because Integrals is not part of the material of my current course.

And that's one of the reasons we ask that people show what they have tried: we have no idea what concepts you have available to do this.

You might try the Mean Value Theorem. I hope you know what that is!

 

[shgidi]

Ok, Ill try again... this is a question from a test I had. The course is calculus 1, and I have for use all of the basic theorems, including mean value, lagrange etc..

I tried some variations of those theorems, but I still have no solution.
Ill be REALLY glad to see a solution.

thanks.

 

[epenguin]

Are you able to treat the case = instead of >= ?

Do that and then try to think about > .

 

[ice109]

Are you able to treat the case = instead of >= ?

Do that and then try to think about > .

you don't need to prove the >, if = is satisfied on the interval then the theorem is true. how is this not simply true definition since e^x's derivative is itself hence g(x)=e^x=g'(x)