There are multiple ways to find the point of inflection of a function:
Manually:
- Find the second derivative of the function.
- Set the second derivative equal to zero and solve for x. This will give you the potential inflection points.
- Evaluate the second derivative for each potential inflection point. If the second derivative changes sign at that point, it is a true inflection point. If it doesn't change sign, it isn't.
Using graphing tools:
- Graph the function using a graphing calculator or software.
- Look for points where the function changes concavity. These are the potential inflection points.
- Use the graphing tool's features to pinpoint the exact x-coordinates of these points.