Answer
$$ \dfrac{48}{(1025)^{3/2}}$$
Work Step by Step
We have $$
\kappa(x)=\frac{\left|f^{\prime \prime}(x)\right|}{\left(1+f^{\prime}(x)^{2}\right)^{3 / 2}}=\frac{|12t^2|}{\left(1+(4t^3)^2\right)^{3 / 2}}
=\dfrac{12t^2}{(1+16t^6)^{3/2}}$$
Now, we will compute $\kappa (t)$ at $t=2$
Therefore,
$$
\kappa(2)=\dfrac{12(2)^2}{(1+16(2^6))^{3/2}}= \dfrac{48}{(1025)^{3/2}}$$
