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๐Ÿงฎ Lecture 15 Animations

To start an animation, first click the โ€œโฏ๏ธ Stop animationโ€ button and then click the โ€œโ–ถ๏ธ Start animationโ€ button.


Derivatives and Tangent Lines

Key ideas:

  • \(\frac{df}{dt}(t)\) is the slope of the tangent line to \(f\) at the point \((t, f(t))\).
  • When the slope of the tangent line is negative, increasing \(t\) brings you closer to a minimum.
  • When the slope of the tangent line is positive, increasing \(t\) brings you further away from a minimum.
  • The closer \(t\) is to a minimum, the shallower the slope of the tangent line is โ€“ at a minimum, the slope of the tangent line is 0!

Gradient Descent

Key idea: Depending on (1) the nature of \(f\), (2) the initial guess, and (3) the learning rate, gradient descent may or may not converge to a global minimum!