Multiple continuous functions, solids of revolution?

Posted on 2016-03-26 14:05:00 in Math by BEN

If I want to put multiple functions together to form a continuous function over a defined domain (one with no gaps or sharp edges at all) what do i have to look out for? I don t mean just connecting x^2 with a straight line (unless it was the turning point) as this would not flow. My task is to design a wine bottle using 3 or more functions (through solids of revolution). So the derivatives would need to be equal at the edges of each functions domain but is there a way to do this without trial and error? Thanks

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