the only constant
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i forgot the solution, this only covers the positive/positive case cuz im not a mosochist
A List of all Ongoing Challenge Series
A List of all Ongoing Challenge Series - Lemmy.World
# Active series |No. of posts|Name|Frequency|Difficulty| |—|—|—|—| |25|Siri’s Medium (Inactive) [https://lemmy.world/post/14918354]|Daily|5/10| |5|zkfcfbzr’s unamed series (Inactive) [https://lemmy.world/post/15222597]|Irregular|4/10| If you want to start your own challenge series, create an index post like this one [https://lemmy.world/post/14918354], and let me know in the comments. # Resources - Discord bot [https://monitorss.xyz/] to mirror posts in this community using RSS [https://lemmy.world/feeds/c/dailymaths.xml?sort=New]. - KaTeX [https://katex.org/] so you can include a screenshot of your maths.
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when i first showed this question to my friend, he told me that
f(x) = 0 satisfies the condition. It is incredible that he said this without delay (i have not thought of that possibility at all), but at the same time it made me wanted to explode,
This challenge requires some specific knowledge on the topics, so if you have no idea how to approach this question, take a hint
Initial hintMaclaurin series: openstax.org/books/…/6-introduction
If you found f but not in the specific format
R formula: brilliant.org/wiki/trigonometric-r-method/
No hints on the extension, you are on your own.
[2025/01/15] Twice derivative of function
[2025/01/15] Twice derivative of function - Lemmy.World
## Question - Find the function f such that f'' = -f - Show that the function can be written in format f = A sin(x + B) ## Extension Find a function g such that g'' = C * -g and - g(0) = D - g'(0) = 0 where C and D are arbitrary constants. — ::: spoiler For those who have finished the extension Congratulations, you have just derived the formula for objects in simple harmonic motions [https://en.wikipedia.org/wiki/Simple_harmonic_motion] (physics). :::
Hint
Line of greatest descent is the shortest distance between two contour lines.
I’m sure there are many other ways to solve this, as it is a very open ended question. But anyways this is one of the favourite proof i’ve done
Solution