How is the utility function with constant relative risk-aversion obtained?
In the slide, we're given the marginal utility (or the derivative of the utility function) as $m(x) = x^{-b}$. The utility function whose derivative is $m(x)$ is

\begin{eqnarray*} u(x) =  \int m(x) dx = \int x^{-b} dx = \begin{cases} \frac{1}{1- b} x^{1-b} &amp; \text{when } b \neq 1 \\  \ln x &amp; \text{when } b = 1 \end{cases} \end{eqnarray*}

Verify that $u'(x) = m(x)$.