Mathematics

Inflection points occur where the concavity of a curve changes, which happens when the second derivative equals zero and actually changes sign. For a cubic like this, find $f''(x)$ by differentiating twice, set it equal to zero to find candidates, then verify the sign of $f''(x)$ switches on either side of each candidate—that's your inflection point.

Inflection points occur where the concavity of a curve changes, which happens when the second derivative equals zero and actually changes sign. For a cubic like this, find $f''(x)$ by differentiating twice, set it equal to zero to find candidates, then verify the sign of $f''(x)$ switches on either side of each candidate—that's your inflection point.