ISSN: 2250-3005 - ijcer

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2Issue. 8The equation of the tangent at point x 0 = e1isy = (k + e)x − 2Then, this tangent is line passing through the point N(1 ,k -1) and the point P (0, −2) .e e1Hence, we obtain the following algorithm to plot geometrically the tangent at x 0 =eAlgorithm:• Plot the line y = kx and the line x = e1;• Mark the point M which is the intersection of the last two lines;• Plot the point N which is image of the point M by the translation of vector t .In this case, the tangent at x 0 = e1is the line (PN) (see figure 4).j Figure 4. Tangents of the family f k (x)= kx + ln(x) at x 0 =e12.5 Tracing the curves y = kx + ln(x) from bundles of tangentsIn this new learning situation, we give to student the algorithms of the tangents of a family of functions f k ,k IR, at the following points x 0 = 11, x0 = 1, x k0 = e and x 0 = . And we demand to student to plot the curves of fk ,ek IR. In the second part of this situation, the student is informed that this family of function is f k (x) = kx + ln(x),k IR, and we demand him to focus on the graphical representation of the function f 0 in order to find the properties ofthis function (domain of definition, convexity, monotony, boundary limits,...). Thus, this new learning situation canpresent the logarithm function at high school.Issn 2250-3005(online) December| 2012 Page 99