Core concepts

• Limit and continuity intuition.
• Derivative as rate of change and slope.
• Rules: product, quotient, chain rule.
• Increasing/decreasing function tests.
• Maxima-minima conditions.

Fast-solving order

1. Check if direct substitution works.
2. If not, factorize or rationalize.
3. Differentiate stepwise and simplify before substitution.

Common mistakes

• Applying L'Hospital-type thinking where algebraic simplification is enough.
• Sign errors in chain rule.
• Using first derivative test incorrectly at stationary points.