Ask about global maximum and global minimum? The temperature distribution in a metal rod given by the following function of the position $x \in \mathbb{R}$: $$T(x) = \frac{1 + 2x}{2 + x^2}$$
What is the maximal and minimal temperature in the metal rod?
$T'(x) = 0$ when $x = 1$ or $x = -2$. But I can't calculate the global maximum and global minimum because $T(x)$ does not belong to any intervals? Am I correct?
Thank you. 

Assuming your work on the derivative is correct (I haven't checked), since $T$ is continuous:
\begin{align}
T(1)&=1\\
T(-2)&=-\frac{1}{2}\\
T(-\infty)&=T(+\infty)=0
\end{align}
So there you have: global max at $x=1$ and global min at $x=-2$. 
