), she realized she was at a critical point that was neither a peak nor a valley. She had to push past the equilibrium to find the true summit. The Lagrange Constraint
—prevented her from walking directly to the center. She had to find the highest point within the boundary. Multivariable Calculus with Analytic Geometry, ...
). At that precise alignment, she found the maximum elevation allowed by the law. The Analytic View ), she realized she was at a critical
Sora began at the base. To find the fastest way up, she used her . "The gradient vector She had to find the highest point within the boundary
always points toward the steepest ascent," she reminded herself. Every step she took was in the direction of the greatest change. If she turned 90 degrees, she’d be walking along a , staying at the exact same altitude—safe, but getting nowhere. The Fog of Partial Derivatives