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Show that, given any three points of $R^{n}$, there is a differentiable path through these three points.

I'm having difficulty solving this problem. I'm trying to solve this problem as follows: Let $a,b,c \in R^{n}$. Taking two straight paths connecting a and b, b and c. Note that b is not differentiable. My idea was to try to reparametrize this path in order to make it differentiable at this point, but I am have difficulty. Could someone help me? Thank You!

user137153
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    Since three points lie in a plane, you can simplify the problem and only consider three points in R^2. Maybe just find a parabola that goes through them? Or use the so-called "Bezier curves" or whatever that programmers use? – user140943 Apr 08 '14 at 03:03

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Hint: Actually three points are in a plane. So we can just consider the situation in $\mathbb R^2$.

gaoxinge
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Like others said, there is a plane containing the three points. Now, given three points, you can find a circle going through these three points. Restrict the circle to a path going through the three points and you have your smooth path.

DBFdalwayse
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