Find the curvature of r(t) = 9t. t2. t3 at the point (9. 1. 1).

curvature is | r’ x r”| / | r’ | ^3
r'(t) = <9,2t,3t^2>
r”(t) = <0,2,6t>
r’ x r” = <6t^2 , -54t , 18>
at t = 1 , |r’ x r”| = sqrt(6^2 + 54^2 +18^2) = 57.24
|r’| = 9.7
| r’ x r”| / | r’ | ^3 = 57.24/9.7^3 = 0.063

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