information to the user similarly circular member 40 b represents the point x u03b4x f x u03b4x and label 26 is positioned nearby to indicate this vertical strings 34 are shown with attachment means 36 coupled to circular members 40 a and 40 b such that vertical strings 34 extend in the y direction of the graph rectangular markers 42 are placed at locations along the x axis 46 to identify the positions of the circular markers 40 a and 40 b label 28 is positioned on the substrate 12 between the lengths of the vertical strings 34 to identify that the distance between circular member 40 a and 40 b is represented by the value u03b4x further two additional rectangular markers 42 are placed along the y axis of the graph to represent the positions f x and f x u03b4x and labels 18 and 24 are located nearby to identify each position in fig2 movable rod 38 is configured to define a secant line extending between circular markers 40 a and 40 b a secant line is a straight line that intersects a curve at two or more discrete points along the curve the slope of the secant line represents the average rate of change and is defined by u03b4y u03b4x as such the slope of the secant line shown in fig2 is equal to the f x u03b4x u2212 f x x u03b4x u2212 x or f x u03b4x u2212 f x u03b4x now turning to fig3 the calculus teaching aid 10 of the present invention in operation is shown being used to graphically demonstrate the calculation of the first derivative of the function in mathematics the first derivative represents the instantaneous rate.