# Are the inflection points where f'(x) = zero or where the graph changes from concave up to concave down?

##### 2 Answers

The inflection point is a point where the graph of the function changes from concave up to concave down or vice versa.

To calculate these points you have to find places where

For example to find the points of inflection for

Now we have to check where

We found that **may be** a point of inflection.

To find if it is such point we have to check if

To find this we can graph the function:

graph{42x^5 [-3.894, 3.897, -1.95, 1.948]}

We can see that the

**Note**

It is important to check to see whether concavity actually changes.

Now we have to check where

We found that **may be** a point of inflection.

To find if it is such point we have to check if

But

I have been taught and, following our textbook's lead, I continue to teach , that an inflection point is a point **on the graph** at which the concavity changes.

#### Explanation:

Using this terminology:

For

The function:

The concavity is not the same on the entire graph, but there is no inflection point, because there is no point on the graph at