In this app, a standard example for introducing the derivative is presented. The square function and the fixed point P(1|1) on the graph are given. The point Q can be shifted on the graph by dragging the mouse. The tangent at P is marked red, the (variable) secant through P and Q is marked blue. To get the most accurate approximation of the tangent slope, you must move the point Q along the curve to the point P. However, if Q is choosen exactly equal to P, the secant slope is not defined (division by 0). The tangent slope is therefore defined as the limit of the secant slope.
The slider allows to get the tangent slope also for another point P.