The concept of derivative

Calculus, as a discipline, grew out of four major problems seventeenth-century mathematicians were wrestling with:

1. The tangent line problem — given a curve and a point on it, what does it even mean for a line to be "tangent" there, and how do we find its slope?
2. The velocity and acceleration problem — given a position function of time, what is the object's instantaneous velocity (and, from that, its acceleration)?
3. The minimum and maximum problem — where does a quantity that varies continuously reach its largest or smallest value?
4. The area problem — how do we find the exact area under a curved boundary? …