A function f(x) has its own graph.

The slope of the tangent to the graph at any point on it is given by the derivative of the function f ' (x)

Hence at a given point x = a , the slope of the tangent is equal to f '(a).

For example, for the function f(x) = x^{2} , f '(x) = 2x, which gives the slope of the tangent at x.

Hence at the point x =3 , the slope of the tangent is 6.