# How do you find all points of inflection given #y=2x^2+4x+4#?

##### 1 Answer

Oct 29, 2017

There are no points of inflection.

#### Explanation:

Points of inflection are places where the concavity of a function changes. Analytically, this happens when the sign of the second derivative

We first find

The second derivative is a constant value (4), meaning that the second derivative is defined always (it's 4), and it will never change sign. Thus, there are no points of inflection. This is demonstrated also by the graph, which is a "bowl up" parabola, and thus never changes from bring "bowl up" to "bowl down".