
Visualiing Derivatives with Cubes
Posted:
Sep 1, 2013 12:37 PM


Its easy to visualize what's going on with the derivatives of x**2 and x**3 with the usual square and cube representations of those functions: a square can be enlarged by "building out" along two edges, a cube can be likewise by "building out" on three faces  the "error" artifacts are the little dx corner square in the 2D case, the corner cube as well as the three edge "lines" in the 3D case. Its just a cute way of seeing where the derivatives d/dx(x**2) = 2x, and d/dx(x**3) = 3(x**2) come from.
But I don't see how to do anything similar with triangles or tetrahedrons. Perhaps Kirby will show us. Or does this simple exercise point to something a bit more fundamental than simple "cultural choice"?
Cheers, Joe N

