CALCULUS FOUNDATIONS
From a secant line
to a derivative.
Gradient descent is built on a simple question: if I nudge the input, how much does the output change?
THE LIMIT IN MOTION
Watch the second point approach a
tangent at a secant across Δx sample points
WHY THIS MATTERS FOR AI
Training follows the slope downhill.
A model changes its parameters in the direction that reduces the loss. Derivatives tell it which small changes help—and by how much.
θ ← θ − α · ∇θ J(θ)