Timeline for How to show continuity and monotonicity of solutions to this parametrized equation?
Current License: CC BY-SA 4.0
5 events
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| Sep 14, 2020 at 14:12 | comment | added | Iosif Pinelis | @AsafShachar : I did miss that term. However, now the solution is only a bit simpler. I have also added details. | |
| Sep 14, 2020 at 14:10 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 76 characters in body
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| Sep 14, 2020 at 7:46 | comment | added | Asaf Shachar | This seems like a nice solution, thanks. I am sorry to bother you, but if I am not mistaken, the rewriting of the equation should be $G(r,y):=2^r y^{2 r-1} (r+y-ry)-1=0, $ instead of $G(r,y):=2^r y^{2 r-1} (r+y)-1=0. $ (you have a missing term of $ry$ coming from the multiplication of the original equation by $\sqrt s=1-y$). I was able to verify all the steps after this modification, except for the last one which concerns the sign of $G'_r$. | |
| Sep 13, 2020 at 17:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 67 characters in body
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| Sep 13, 2020 at 15:58 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |