Orby chat
A tutor that shows, not just tells
Orby is your AI study partner. Ask a question and it answers in clear prose. When it helps, it draws graphs, builds interactive quizzes, generates flashcards and renders tables and equations right in the conversation. Link your own chapters so it grounds its answers in your material.
Explain Rolle’s theorem to me
If f is continuous on [a, b], differentiable on (a, b) and f(a) = f(b), then there is a c in (a, b) with f′(c) = 0: the tangent is horizontal there.
Example: f(x) = x² − 4x satisfies f(1) = f(3) = −3, and indeed f′(x) = 2x − 4 vanishes at c = 2.
What does Rolle’s theorem guarantee?
Correct. Rolle gives you that c exists, not its value.
What you get
Rich answers: graphs, quizzes, flashcards, tables and maths inline
Ground answers in your own chapters and documents
Attach photos and PDFs for Orby to read
Streamed replies, edit your messages, regenerate anytime
Good to know
Yes. Link a chapter with the + button and Orby uses it as a read-only reference for its answers.
Fully. Orby renders inline and display equations, and can plot functions interactively.