Chapter 4.5, Problem 73E

To determine

(a)

To prove:

$f\left(0\right)$ is local maximum and $f\left(2\right)$ a local minimum.

To determine

(b)

Toprove:

$f$ is concave down on $\left(-\infty ,1\right)$ and concave up on $\left(1,\infty \right)$.

To determine

(c)

Toprove:

$\underset{x\to 1-}{\lim }f\left(x\right)=-\infty$ and $\underset{x\to 1+}{\lim }f\left(x\right)=\infty$

To determine

(d)

Toprove:

$y=x+1$ is a slant asymptote of $f$ as $x\to \pm \infty$.

To determine

(e)

Toprove:

The slant asymptote lies above graph of $f$ for $x<1$ and below the graph for $x>1$.