Teorema de Darboux

[@joaquinborbas6630]

🎯 Key points for quick navigation: 📚 Darboux's Theorem is discussed, relating to the behavior of derivatives, even if they're not continuous. 🔍 The theorem indicates there's a value within an interval where the derivative image is the derivative itself. 🎯 The proof involves showing that points in the interval are not extremes but within the interior. 🚫 It's impossible for the derivative to exist at the interval's endpoints. 🎢 The analysis uses right and left derivatives to establish logic and contradiction. 🧩 The argument also demonstrates that a derivative cannot be strictly positive or negative over an interval. 🔄 A key part of the proof is confirming the derivative at a certain point is zero, leading to conclusions about the theorem. 🏁 Ultimately, the proof verifies the intermediate value property of derivatives, reinforcing Darboux's Theorem. Made with HARPA AI

[@TheStickman2014]

derivda entonces tambien debe ser continua , porque dices que no?

[@StarMaths]

hola como estas, perdón por la demora. En este caso la derivada no necesariamente debe ser continua, si así lo fuere simplemente aplicamos el teorema de valor medio y el teorema de Darboux estaría demostrado, pero lo interesante de este teorema es que a pesar que la derivada no es continua igualmente para todo "d" en f'(a)

[@daniloramos9103]

Cuando dices que hay una delta que tendrá puntos menores que el mínimo, la derivada tiene que ser continua, lo cual no es el caso.