A parabolic segment is bounded by chord AB and the parabola f(x)=ax^2, and its area is shown. Also shaded in the graph is the triangle ABC and the rectangle ABDE - and their respective areas are shown.

Point C on the parabola is the point at which the slope of the tangent line (derivative) is equal to the slope of chord AB. The line segment ED (one side of the rectangle ABDE) is tangent to the parabola at C.