To find the points of inflection, we must find the points at which the second derivative of the function changes sign.

First, we must find the second derivative:

The derivatives were found using the following rule:

Next, we must find the x value at which the second derivative is equal to zero:

Using this value, we make our intervals on which we examine the sign of the second derivative:

Note that at the endpoints of the intervals, the second derivative is neither positive nor negative.

Now, simply plug in any value on the interval into the second derivative function and check the sign. On the first interval, the second derivative is negative, while on the second interval, it is positive. Thus, a point of inflection exists at . To get the y-coordinate, simply evaluate the function at this x value:

The point of inflection is .

To determine the points of inflection, we must determine the x values at which the second derivative changes in sign.

So, we must first find the second derivative:

The derivatives were found using the rule

Next, we must find the values at which the second derivative is equal to zero:

Now, using this zero, we can make the intervals on which we check the sign of the second derivative:

Note that at the endpoints, the second derivative is neither positive nor negative.

Plug in any value on each interval into the second derivative function and check the sign. On the first interval, the second derivative is negative, while on the second, it is positive. Because a sign change occured at , there exists the point of inflection.

To determine the points of inflection of the function, we must determine where the second derivative of the function changes sign.

First, we find the second derivative:

The derivatives were found using the following rule:

Now, we must find where the second derivative equals zero:

Using this value, we can now create the intervals on which we check the sign of the second derivative:

Note that at the endpoints of the intervals, the second derivative is neither positive nor negative.

To check the second derivative's sign on each interval, simply plug in any point on the interval into the second derivative function. On the first interval, the second derivative is negative, while on the second interval, it is positive. Because the sign of the second derivative changes at , there exists the point of inflection.

Infelction points are the points of a graph where the concavity of the graph changes.  The inflection points of a graph are found by taking the double derivative of the graph equation, setting it equal to zero, then solving for .  

To take the derivative of this equation, we must use the power rule,

 .  

We also must remember that the derivative of an constant is 0.  

After taking the first derivative of the graph equation using the power rule, the equation becomes

.  

In this problem the double derivative of the graph equation comes out to , factoring this equation out it becomes .  

Solving for when the equation is set equal to zero, the inflection points are located at .