## Quick Reference

The real function *f* of one variable is differentiable at *a* if (*f* (*a*+*h*)−*f* (*a*)/*h* has a limit as *h* → 0; that is, if the derivative of *f* at *a* exists. The rough idea is that a function is differentiable if it is possible to define the gradient of the graph *y*=*f* (*x*) and hence define a tangent at the point. The function *f* is differentiable in an open interval if it is differentiable at every point in the interval; and *f* is differentiable on the closed interval [*a*, *b*], where *a* < *b*, if it is differentiable in (*a*, *b*) and if the right derivative of *f* at *a* and the left derivative of *f* at *b* exist.

*Subjects:*
Mathematics.