$e^x \le x+ e^{x^2}$ for $x\in \mathbb{R}$.
I'm struggling to show this inequality. I've tried differentiation but to no avail. How can I show this? I would greatly appreciate some help.
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3This question was asked before: Proof of inequality $e^x\le x+e^{x^2}$ and Proof of the inequality $e^x\le e^{x^2} + x$. (And maybe some other posts, but these two I was able to find quickly.) – Martin Sleziak Jan 11 '16 at 06:12
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I have a different proof that using Lagrange Mean value theorem. – Subham Jaiswal Jan 11 '16 at 06:34
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I mean my proof is different from the ones provided in the other links. – Subham Jaiswal Jan 11 '16 at 06:36
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@MosBlack Well, then go ahead and post it into some of the questions about this inequality. (Unless there already is an answer with such approach.) Maybe there are more copies of this problem on this site, but we have at least the questions linked from here. – Martin Sleziak Jan 11 '16 at 06:37
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1@MosBlack I will add that some of them might be closed as duplicates too. (Thanks to this question we discovered several posts asking basically the same thing.) So you should keep that in mind. If when you finish writing answer you find out that the post has already been closed and the answer cannot be posted there, you can still copy and post it to the one which remained open. – Martin Sleziak Jan 11 '16 at 06:42