1
$\begingroup$

Can it be shown that when $$\mathbb{R}_0^+\colon=[0,\infty[$$ for all $$x\ge0$$ that $$\ln(x+1)\le x$$ so far I have shown $$f{'}(x)= \frac{1}{1+x}-1<0$$ hence function is monotonically decreasing and has a global maximum at $$x=0$$

$\endgroup$
0
$\begingroup$

You are almost there. Simply add this line to your last line of proof:

$f(x) \leq f(0) \to \ln(1+x) - x \leq 0 \to \ln(1+x) \leq x$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.