Calculus theorems, hypothesis by hypothesis

Knowing what a theorem says is the easy half. The half that decides whether you can use it is knowing what each condition is holding up, and what breaks the moment one is missing. Every page here states the theorem formally, then drops each hypothesis on its own and shows the function that breaks the conclusion.

27 counterexamples across 22 theorems, each one evaluated numerically on every build. A counterexample that stopped failing the conclusion would fail the build instead of quietly misleading a reader.

AP Calculus AB and BC

• Mean Value Theorem2 hypotheses, 2 checked counterexamples
• Rolle's Theorem3 hypotheses, 3 checked counterexamples
• Intermediate Value Theorem2 hypotheses, 1 checked counterexamples
• Extreme Value Theorem3 hypotheses, 2 checked counterexamples
• Squeeze Theorem2 hypotheses, 1 checked counterexamples
• Differentiability implies continuity1 hypothesis, 1 checked counterexamples
• Fundamental Theorem of Calculus, Part 12 hypotheses, 1 checked counterexamples
• Fundamental Theorem of Calculus, Part 22 hypotheses, 1 checked counterexamples
• L'Hopital's Rule3 hypotheses, 2 checked counterexamples
• Mean Value Theorem for Integrals2 hypotheses, 1 checked counterexamples
• Derivative of an inverse function2 hypotheses, 1 checked counterexamples
• Interior Extremum Theorem3 hypotheses, 1 checked counterexamples
• Second Derivative Test2 hypotheses, 1 checked counterexamples
• Increasing/Decreasing Test2 hypotheses, 1 checked counterexamples
• Limit Laws2 hypotheses, 1 checked counterexamples
• Chain Rule2 hypotheses, 1 checked counterexamples

BC only

• nth Term Test for Divergence1 hypothesis, 1 checked counterexamples
• Geometric Series Theorem2 hypotheses, 1 checked counterexamples
• p-Series Theorem2 hypotheses, 1 checked counterexamples
• Alternating Series Test2 hypotheses, 1 checked counterexamples
• Absolute Convergence Theorem1 hypothesis, 1 checked counterexamples
• Taylor's Theorem with Lagrange Remainder2 hypotheses, 1 checked counterexamples