An inflection point is any point on a graph of a function where the concavity of the function changes (ie. from concave up to concave down). For a function to have an inflection point it must have a second derivative. Inflection points can be found on a graph by checking for locations where the second derivative switches signs.

Example

Given the function find the inflection points

is shown in blue and the second derivative of is also shown in green.

Checking right before the potential inflection point

Checking right after the potential inflection point

	Concave Down	Inflection Point	Concave Up

Non-Example

Given the function find any inflection points

is shown in blue and the second derivative of is also shown in green.

Checking right before the potential inflection point

Checking right after the potential inflection point

There are no inflection points on the graph of the function