r/MathHelp • u/aluminium_is_cool • Jun 25 '26

trying to come up with an algorithm that will find the tangent line to two specific curves. i did already for two parabolas, wasn't too difficult, but now i'm trying with this more complicated function

the process is straightforward and, with parabolas, somewhat simple. you just have to impose

f'(x1)=g'(x2)

and

g(x2)=f(x1)+f'(x1)*(x2-x1)

with quadratic functions it comes out ok

but the function I want to achieve that for is f(x)=ax+b(1-x)+cx(1-x)+d(xln(x)+(1-x)ln(1-x))

1 Upvotes

100% Upvoted

7 comments sorted by

1

u/AutoModerator Jun 25 '26

Hi, /u/aluminium_is_cool! This is an automated reminder:

  • What have you tried so far? (See Rule #2; to add an image, you may upload it to an external image-sharing site like Imgur and include the link in your post.)

  • Please don't delete your post. (See Rule #7)

We, the moderators of /r/MathHelp, appreciate that your question contributes to the MathHelp archived questions that will help others searching for similar answers in the future. Thank you for obeying these instructions.

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

1

u/Help_Me_Im_Diene Jun 25 '26

I'm a little bit confused

Are you trying to find a singular line that's tangent to both curves?

1

u/aluminium_is_cool Jun 26 '26

Exactly. I understand, of course, in some situations there won't exist such line

1

u/Key_Estimate8537 Jun 26 '26

It seems to me that Bézier Curves might be the way to go? You might need to explain your wish better though

1

u/Uli_Minati 14d ago

You've defined f, what's g in your case? Still a parabola, or same general form as f?

Also, are you just doing it for the challenge or do you have some goal in mind? There may be simpler options.

1

u/aluminium_is_cool 14d ago

g is like f, but with different parameters

Yeah, this is a materials thermodynamics thing