The graphical features of functions can help us find important points, like local highs and lows, and points where the curve changes direction. Here’s how we can identify these points:

1. Local Extrema:

   • These points happen where the first derivative, written as $f'(x)$, equals zero or is not defined.
   • We can confirm these points using the first derivative test. If the sign changes around a critical point, it shows that we have a local maximum (the highest point nearby) or a local minimum (the lowest point nearby).

2. Points of Inflection:

   • These are found where the second derivative, noted as $f''(x)$, equals zero or isn’t defined.
   • We check for a sign change in $f''(x)$ to confirm that there is a shift in the curve’s shape, which is called concavity.

In summary, looking at these derivatives helps us understand how the function behaves when we look at its graph.