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## Main Question or Discussion Point

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

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

thanx to the solvers

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

thanx to the solvers

- Thread starter shgidi
- Start date

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

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

thanx to the solvers

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

thanx to the solvers

- 1,703

- 5

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

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

we shall prove f(x)>

thanx to the solvers

Gib Z

Homework Helper

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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, [itex]x \geq 0[/itex], 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 :(

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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 does'nt quiet help me, because Integrals is not part of the material of my current course.

HallsofIvy

Science Advisor

Homework Helper

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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.

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 does'nt quiet help me, because Integrals is not part of the material of my current course.

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

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I tried some variations of those theorems, but I still have no solution.

Ill be REALLY glad to see a solution.

thanks.

epenguin

Homework Helper

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

Do that and then try to think about > .

Do that and then try to think about > .

- 1,703

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

Do that and then try to think about > .

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