Condition of continuity of the first derivative

Hi,

i'm not very expert in Matlab and i don't know if i can explain exactly my problem. I try! I have two vectors(x1,x2 and y1,y2) that contain coordinates that describe two branches of curve. I would like to plot a single curve obtained from the union of the two branches.

The issue is that I want to join the two branches so that the overall curve has continuous first derivative at the point of intersection of the two branches (i have found the intersection point by extrapolating outside of the range of definition of the two branches). I need to impose the condition of the derivative in order to avoid the danger that the two branches form a cusp at the point of intersection.

Someone may suggest how to impose the passage for some points and at the same time the continuity of the derivative at a point?

Thanks!!