If $f''(c) > 0$, then $f$ has a relative minimum at $c$.

If $f''(c) < 0$, then $f$ has a relative maximum at $c$.

If $f''(c) = 0$ or is undefined, the test is inconclusive (use First Derivative Test).

Steps for Curve Tracing (Graphing):
1. Find domain, intercepts (x- and y-).
2. Check for symmetries (even/odd).
3. Find asymptotes (vertical, horizontal, slant).
4. Find $f'(x)$: Determine critical numbers, intervals of increase/decrease, relative extrema (using First Derivative Test).
5. Find $f''(x)$: Determine intervals of concavity, inflection points (using Second Derivative Test if applicable).
6. Plot key points (intercepts, extrema, inflection points) and sketch the graph using the information gathered.
Graph of $f$ from $f'$:
- If $f'(x) > 0$, $f(x)$ is increasing.
- If $f'(x) < 0$, $f(x)$ is decreasing.
- If $f'(x) = 0$ and changes sign, $f(x)$ has a local extremum.
- If $f'(x)$ is increasing, $f(x)$ is concave up ($f''(x)>0$).
- If $f'(x)$ is decreasing, $f(x)$ is concave down ($f''(x)<0$).
- Points where $f'(x)$ has a local extremum correspond to inflection points of $f(x)$.

Absolute Extrema: The maximum or minimum value a function takes over its entire domain or a specified interval.
- Absolute Maximum: $f(c)$ is an absolute maximum if $f(c) \ge f(x)$ for all $x$ in the domain.
- Absolute Minimum: $f(c)$ is an absolute minimum if $f(c) \le f(x)$ for all $x$ in the domain.
Extreme Value Theorem (EVT): If $f$ is continuous on a closed interval $[a, b]$, then $f$ attains both an absolute maximum value and an absolute minimum value on that interval.
Finding Absolute Extrema on a Closed Interval $[a, b]$:
1. Find all critical numbers of $f$ in $(a, b)$.
2. Evaluate $f$ at all critical numbers found in step 1.
3. Evaluate $f$ at the endpoints $a$ and $b$.
4. The largest of these values is the absolute maximum, and the smallest is the absolute minimum.

Rates of Change: The derivative $f'(x)$ represents the instantaneous rate of change of $f(x)$ with respect to $x$.
Rectilinear Motion (Motion along a line):