Answer
\[
\left(-\frac{1}{2} \ln 2,1 / \sqrt{2}\right)
\]
Work Step by Step
We find:
\[
\begin{array}{l}
\frac{\left|\frac{d^{2} y}{d x^{2}}\right|}{\left(\left(\frac{d y}{d x}\right)^{2}+1\right)^{3 / 2}} \quad =\kappa \\
\frac{e^{x}}{\left(1+e^{2 x}\right)^{3 / 2}}=\kappa(x)
\end{array}
\]
$C A S: \quad \kappa^{\prime}(x)=\frac{e^{x}\left(1-2 e^{2 x}\right)}{\left(1+e^{2 x}\right)^{5 / 2}}$
\[
\begin{array}{l}
\kappa^{\prime}(x)=0 \text { when } \\
e^{2 x}=1 / 2 \\
x=-(\ln 2) / 2
\end{array}
\]
By the first derivative test, at $x=-(\ln 2) / 2, \kappa$ has a maximum.
The point is:
\[
\left(-\frac{1}{2} \ln 2,1 / \sqrt{2}\right)
\]
