given that f(x) = e^x - x - 1, show that f is an increasing function for x>0

OK i can see that this statement is true... but i just don't know how to write it on paper...

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- May 9th 2009, 04:34 AMdjmccabieeasy function question ?
given that f(x) = e^x - x - 1, show that f is an increasing function for x>0

OK i can see that this statement is true... but i just don't know how to write it on paper... - May 9th 2009, 04:55 AMbobby

Do you not just differentiate it, and show that is is > 0 on $\displaystyle (1,\infty)$??

So $\displaystyle f'(x) = e^x - 1$

$\displaystyle e^x > 0 $ and $\displaystyle e^x > 1 $ for x > 0

$\displaystyle f'(x) > 0 $ for $\displaystyle x>0$

Therefore

$\displaystyle f(x) $is an increasing function..

Sound right?