# What is different between critical point and inflection point?

##### 1 Answer

There seem to be two definitions of "critical point" in use. But with that in mind:

#### Explanation:

A **critical number** for function

These are the numbers at which Fermat's Theorem on local extrema tells us

In some usages "critical point" is synonymous with this "critical number".

In other usages a critical point is a point

An **inflection point** for the graph of function

For twice differentiable functions, this is a point on the graph of

Students sometimes use "inflection point" to mean an

The difference is illustrated by

In the "point" usage, the graph has no inflection point, because there is no point **on the graph** where concavity changes.