'smoooth joining' - WTF

[heylex]

in a little bit of panic about my methods SAC tomorrow, and i'm a little confused about the 'smooth joining of points'

our teacher has done basically nothing on it, but told us it will be on our sac...so i was wondering if i had the basics right:

two different graphs can only 'connect' smoothly if they had the same gradient ()
and if the gradients are different, then there is a 'sharp point' and the gradient at that point is 0....

is there anything else i should know??? :S :S

[kensan]

It is smooth if the gradient is the same at a given point, and if the function is continuous at that point.
Most likely you will get a hybrid function and at a given x value, would need to work out some variables so the function is 'smooth and continuous' at that point.
I could make a sample Q if you want

[fred42]

You are correct that the gradient of each of the 2 graphs at the join must be smooth and the curve must be continuous. However, if not, the gradient is NOT zero - it is not differentiable at that point.