You can change the function f (plotted in green) on the left-hand side. The derivative (shown also on the left) is calculated automatically and is plotted in blue.[br]It is possible to move the coordinate plane and to zoom in (e.g. by using the scroll wheel on your mouse). [br]You can change x_0 by using the slider on the top right of the GeoGebra window. It is the x-coordinate of the (black) point on f, in which the tangent line t (in red) and normal line n (in yellow) to f are plotted. Their expressions are shown on the right-hand side.[br][br]The key issue here:[br]In order to calculate t and n to f in x_0 you need the slope of f in x_0, which is f’(x_0). It is the value of the derivative of f in x_0. Instead of calculating this value, one could also look it up on the blue graph f’, on which the relevant point is marked as a blue point.