Calculus
Maxima and minima: laboratory
Ten cases distinguish free extrema, boundaries and constraints. Select candidates, explore the surface and trace the boundary: graphics aid understanding; formulas justify conclusions.
Function and feasible set
Candidates and proved results
Surface and candidate points
Blue surface; orange path; red candidates; black selected point. Map: approximate levels, not mathematical proof.
Map: click to choose a point
Trace the boundary / a test curve
One move each second. The path returns to its starting point after 24 moves. On a rectangle the slider measures perimeter fraction, not geometric angle.
Value along the path
Guided cases with analytically calculated candidates, not a general symbolic solver. The graphics window does not limit the free domain. Decimals are rounded.