Compute the curvature κ\kappaκ of the parametric curve r(t)=(t,t2)\mathbf{r}(t) = (t, t^2)r(t)=(t,t2) at t=1t = 1t=1. Use the formula κ=∣x′y′′−x′′y′∣(x′2+y′2)3/2\kappa = \frac{|x'y'' - x''y'|}{(x'^2 + y'^2)^{3/2}}κ=(x′2+y′2)3/2∣x′y′′−x′′y′∣.
255\frac{2}{5\sqrt{5}}552
25\frac{2}{5}52
52\frac{\sqrt{5}}{2}25
15\frac{1}{\sqrt{5}}51