## Quick Reference

(of a curve)

The gradient of a curve at a point *P* may be defined as equal to the gradient of the tangent to the curve at *P*. This definition presupposes an intuitive idea of what it means for a line to touch a curve. At a more advanced level, it is preferable to define the gradient of a curve by the methods of differential calculus. In the case of a graph *y*=*f*(*x*), the gradient is equal to *f*′(*x*), the value of the derivative. The tangent at *P* can then be defined as the line through *P* whose gradient equals the gradient of the curve.

*Subjects:*
Mathematics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.