Calculus Review for Optimization

Optimization · Axiom Academy

INTRO Calculus Review for Optimization Discover how derivatives, gradients, and curvature guide us to optimal solutions. Move the point along the curve to see how the derivative (slope) changes. Where does the slope equal zero? Explore different points where the derivative is zero. Notice how the slope changes on either side. Gradients: Direction of Steepest Ascent Drag the point around the surface. The gradient arrow shows the direction of steepest increase. The Hessian: Understanding Curvature Adjust the curvature parameters to see how second derivatives determine whether a critical point is a minimum, maximum, or saddle point. Find critical points by setting ∇f = 0. These are candidates for optima where the slope is flat in all directions. Classify critical points using curvature. Positive definite Hessian → minimum. Negative definite → maximum. Indefinite → saddle point. Move opposite to the gradient direction to descend toward a minimum. The gradient tells us which way is "downhill" at every point.

This is the written version of the interactive lesson above. See the full Optimization course.