Calculus
Continuity and theorems lab
Check assumptions, repair a join, find intermediate values and distinguish attained extrema from limiting bounds.
Graph and included/excluded points
Filled point = included; open circle = excluded. Finite view: not a proof; very dense oscillations cannot be resolved on screen.
Bisection: one halving per second
Value table
Classifications and values come from formulas for these guided cases, not graph pixels. This is not a general symbolic solver.