(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.