Students are already familiar with the idea of tracing a curve by giving different values to x
and finding corresponding values of y and joining these points by free hand curves. But this
type of tracing gives us only a rough idea of what the graph looks like. But to have more
accuracy in sketching the curves we will now use the techniques of domains, intervals of
increase and decrease of the curve, maxima, minima, concepts of concavity and convexity,
asymptotes etc. Many of these techniques are already studied in details by the students in
lower classes but some of these like concavity convexity, asymptotes, multiple points are new
to them. So first of all we will have discussion about these new topics.