Analysis · Calculus
Differentiation — Rigorous Treatment
The MVT — the average rate of change is achieved at some interior point — is the engine of differential calculus. Taylor’s theorem gives rigorous polynomial approximation error bounds.
WHAT STUDENTS WILL LEARN
✓Define the derivative rigorously; prove differentiation rules
✓State and prove the Mean Value Theorem
✓Apply Taylor’s theorem with Lagrange remainder
✓Connect differentiability to local linear approximation
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