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What are real functions f() if f'(x)=2x+1 and f(0)=0?

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ruals | Salutatorian

Posted July 13, 2013 at 3:14 PM via web

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What are real functions f() if f'(x)=2x+1 and f(0)=0?

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aruv | High School Teacher | Valedictorian

Posted July 13, 2013 at 3:22 PM (Answer #1)

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 Given problem is

`f'(x)=2x+1`  and `f(0)=0`

Let us assume that `f'(x)` is well behaved i.e. it is integrable

Integrate

`intf'(x)dx=f(x)`

so

`f(x)=int(2x+1)dx +c`

`f(x)=2x^2/2+x+c`

`f(x)=x^2+x+c`  ,where c is integrating constant

By given condition

`f(0)=0=0^2+0+c`

C=0

Thus real function is

`f(x)=x^2+x`

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