🧮 Lecture 10 Animations

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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 – at a minimum, the slope of the tangent line is 0!

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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!