In calculus II, vector valued function in space. The vector function r(t)=f(t)i+g(t)j+h(t)k. The curve traced by r is smooth if dr/dt is continuous and NEVER 0.
I don't understand why there is "NEVER 0" in the above statement, in order for the curve traced to be smooth.
The Attempt at a Solution
The original statement appear in texts such as Thomas/Finney Calculus, Davis (introduction to vector analysis). But their explanations are very different. In learning calculus I, a smooth curve does not seem to require dy/dx=0 (e.g. y=x^3 is a smooth everywhere). Why in dealthing with vector calculus, there is such restriction.