Mathematics · Grades 11–12
Calculus: meaning, conditions and checks · revision card
A derivative describes local rate of change where it exists.
Keep these ideas clear
Derivative
A derivative describes local rate of change where it exists.
Integral
A definite integral accumulates signed contribution; geometric area may require separating signs.
Two useful examples
The derivative of a constant function is
0
0
For f(x) = x³, find f′(2).
f′(x) = 3x²; 3 × 2² = 12.
12
Explain it without looking
- Explain why total distance may require integrating absolute velocity rather than velocity.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.