draw graphs using derivative tests

Derivative tests can be used to approximate the graph of $f(x)$ by determining (local/absolute) extrema and concavity.

• Identify asymptotes before differentiation (e.g. variable in the denominator)
• Note: If $f(x)$ is defined over a closed interval $[x_1,x_2]$, then $f(x)$ has an absolute maximum or minimum in $[x_1,x_2]$. All absolute max/min occurs at $f^{\prime }(x)=0$ or at the end points ($x\in \{x_1,x_2\}$)
• Note: if there is a variable in the denominator, find the critical point (solve for denominator $=0$)