Given that the asymptotic mean integrated squared error for the histogram with bin width \(h\) is given by

\[\operatorname{AMISE}\left(\bar{f}_{n}, fight)=(n h)^{-1}+\frac{1}{12} h^{2} R\left(f^{\prime}ight),\]

show that the value of \(h\) that minimizes this function is given by

\[h_{\mathrm{opt}}=n^{-1 / 3}\left(\frac{6}{R\left(f^{\prime}ight)}ight)^{1 / 3} \text {. }\]