Points of Inflection (Leaving Cert Mathematics): Revision Notes

Points of Inflexion

A point of inflection is a point on the graph of a function where the concavity of the graph changes. In other words, it is where a curve transitions from being concave up (shaped like $\cup$) to concave down (shaped like $\cap$), or vice versa.

• A function is concave up when its graph bends upwards, and the second derivative is positive $f''(x)>0$.
• A function is concave down when its graph bends downward, and the second derivative is negative $f''(x)<0$.
• At the point of inflexion, the concavity changes which implies that $f''(x)$ either crosses zero or becomes undefined.

Example

Example