1) Let $f(x) = \frac{x^2}{x - 1}$ (Figure 24). Verify the following:
(a) $f(0)$ is a local max and $f(2)$ a local min.
(b) $f$ is concave down on $(-\infty, 1)$ and concave up on $(1, \infty)$.
(c) $\lim_{x \to 1^-} f(x) = -\infty$ and $\lim_{x \to 1^+} f(x) = \infty$.
(d) $y = x + 1$ is a slant asymptote of $f(x)$ as $x \to \pm \infty$.
(e) The slant asymptote lies above the graph of $f(x)$ for $x < 1$ and below the graph for $x > 1$.
