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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: rowshan on November 06, 2008, 02:55:24 pm

Title: anti-derivative graphs for composite functions
Post by: rowshan on November 06, 2008, 02:55:24 pm

when you draw a derivative function for composite functions you have to draw the open circle where the composite functions meet ...
What about when you have to draw the anitderivitive function of a graph, do you have to draw the open circles where the composite functions meet?

Title: Re: anti-derivative graphs for composite functions
Post by: Mao on November 06, 2008, 04:42:41 pm

1. it is not necessary that where the two parts meet, it is not differentiable. It is very possible that the functions may join 'smoothly' [have the same derivative], hence it is continuous AND differentiable and you won't have to draw an open circle.

2. if the above is not the case, the the antiderivative would not exist at that point, though you really wouldn't be asked to graph the antiderivative of a composite function [as each could have a different constant of integration, and they would have to give several initial values and too much work wasted on testing so little], so don't worry.
IN THE UNLIKELY CASE THAT it does come on the exam, then yes, open circles.