Proving calculus' weirdest rule in under 13 minutes

Comments · 103

• GU

  @guyonyt999 · 6 months ago

  obviously its because the apostrophes divide and cancel out

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• R3

  @r3ziakd · 6 months ago

  THIS is what makes me struggle with physics. U technically have the simplest calculations out there, but having to keep the 20 theorems in mind which allow the calculation, while seemingly breaking all rules imposed by mathematics just makes no sense, if even a single theorem is forgotten…

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• TU

  @tulpamedia · 6 months ago

  I swear to god if I have to hear somebody say "hospital rule" one more time im gonna lose it.

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• TH

  @TheLazarusEffect-z64 · 5 months ago

  That clickbait thumbnail worked on me like a charm! (because obviously you need the limit signs and the appropriate conditions listed for it to be true).

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• EV

  @everythingyoudoismuda92 · 6 months ago

  took me a second to realise this was SMVT and not something else at <a href="https://www.youtube.com/watch?v=PvKb2xGeOxE&amp;t=294">4:54</a>

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• MA

  @MarceloKatayama · 6 months ago

  Minor correction, but the extreme value theorem only holds for closed and bounded intervals. Not open.

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• F5

  @f5xs757 · 6 months ago

  rare algorithm pull

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• AL

  @alexismiller2349 · 6 months ago (edited)

  Here&apos;s a very cute way to make the function h appear naturally, and to reduce the computations:<br><br>You want that f&apos;(c)/g&apos;(c) = f(b)-f(a)/g(b)-g(a) right ? Consider the vector v(x)=(f(x),g(x))<br>Geometrically, this is asking that the two vectors v&apos;=(f&apos;(x) , g&apos;(x)) and w=(f(b)-f(a) , g(b)-g(a)) be proportional.<br>Thanks to linear algebra we can write this algebraically as asking that the determinant det(v&apos;,w) be zero.<br>This is the derivative of det(v,w), which is h (up to a constant multiple). From linear algebra it should be clear without calculation that det(v(a),w) = det(v(b),w). And we can conclude the proof as before.

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• MO

  @moviwill · 6 months ago

  mythical algorithmic pull

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• IL

  @iliasp4275 · 6 months ago

  great to see a new channel with real videos and not more AI slop! keep it up!

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• MA

  @mandresyfalimanana3538 · 6 months ago

  Thank you. I love these introductory videos

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• DI

  @diablo6250 · 6 months ago

  how are you so small :( this is such a cool and well put together video.<br>looking forward to more content!

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