## Tip 87. Expanded marking of a Plot

### Fig. 87. Expanded marking of a Plot

In tip 47 we have given you recommendations to put in variables as marker of Cartesian graph instead of numerical constants. It increases “mobility” of the graph: for example, if the marker’s line fixes a root of the function than the variation in the function itself will tell both on the graph and on the lines those fixe the root. Unfortunately in Mathcad we can construct only couple straight lines through the markers on the axes x and y. Apart markers’ lines can not be formatted – we can not change their color, thickness and other attributes that we can change of the graph’s line. Solution of this problem is showed in the fig. 87, where actually not one but five graphs are built: graph of the analyzable function, two vertical lines that fix roots, vertical lines that fixes local minimum and square point that fixes local maximum. The secret of the graph in the fig. 87 is in the notes in the middle of the axes õ and y:

·        axis y: y(x), y(x), y(x), y(x), ymax

·        axis x: x, Rt1, Rt2, Min, Max

Apart the expressions are written in the places of the fixation of the graph’s dispersion of the axis x for whole closure the graph to its “interesting” points (roots and extremes):

·        left side of the axis x: min(Rt1, Rt2, Min, Max) – 0.1

·        right side of the axis õ: max(Rt1, Rt2, Min, Max) + 0.1

After corresponding format of the graph the variations in the function ó(õ) will tell both on position of three vertical lines and one point and on the graph’s dispersion. So that all four “interesting” points do not slip out range of vision of user who analyses the function ó(õ). The main thing here is these points exist and were found by corresponding built-in Mathcad-functions root, Minimize and Maximize.