AHL 5.12 (HL)—Continuity, differentiability and first principles Topic Practice
AHL 5.12 (HL)—Continuity, differentiability and first principles Topic Practice
Practise continuity, differentiability and first-principles derivatives using piecewise functions, limits, constants and derivative definitions.
How this is tested
- compare left and right limits or gradients at a join to test continuity or differentiability
- solve for constants in a piecewise f(x) by enforcing both f and f' at the boundary
- expand [f(x+h)-f(x)]/h and take h→0 to derive a polynomial derivative from first principles