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Example Questions
Example Question #112 : Derivatives
Determine the location of the points of inflection for the following function:
The points of inflection of a function are the points at which its concavity changes. The concavity of a function is described by its second derivative, which will be equal to zero at the inflection points, so we'll start by finding the first derivative of the function:
Next we'll take the derivative one more time to get the second derivative of the original function:
Now that we have the second derivative of the function, we can set it equal to 0 and solve for the points of inflection:
Example Question #1 : Determine Points Of Inflection
Find the points of inflection of the following function:
The points of inflection of a function are those at which its second derivative is equal to 0. First we find the second derivative of the function, then we set it equal to 0 and solve for the inflection points:
Example Question #114 : Derivatives
Find the inflection points of the following function:
The points of inflection of a function are those at which its second derivative is equal to 0. First we find the second derivative of the function, then we set it equal to 0 and solve for the inflection points:
Example Question #115 : Derivatives
Determine the points of inflection of the following function:
The points of inflection of a function are those at which its second derivative is equal to 0. First we find the second derivative of the function, then we set it equal to 0 and solve for the inflection points:
Example Question #116 : Derivatives
Determine the x-coordinate of the inflection point of the function .
The point of inflection exists where the second derivative is zero.
, and we set this equal to zero.
Example Question #117 : Derivatives
Find the x-coordinates of all points of inflection of the function .
There are no points of inflection
We set the second derivative of the function equal to zero to find the x-coordinates of any points of inflection.
, and the quadratic formula yields
.
Example Question #118 : Derivatives
Determine the x-coordinate(s) of the point(s) of inflection of the function .
There are no points of inflection.
Any points of inflection that exist will be found where the second derivative is equal to zero.
.
Since , we can focus on
. Thus
, and
.
Example Question #119 : Derivatives
Find the x-coordinate(s) of the point(s) of inflection of .
There are no inflection points.
The inflection points, if they exist, will occur where the second derivative is zero.
Example Question #1 : Determine Points Of Inflection
Find the point(s) of inflection of the function .
There is no point of inflection.
The point of inflection will exist where the second derivative equals zero.
.
Now we need the y-coordinate of the point.
Thus the inflection point is at .
Example Question #1 : Determine Points Of Inflection
Find the point of inflection of the function .
To find the x-coordinate of the point of inflection, we set the second derivative of the function equal to zero.
.
To find the y-coordinate of the point, we plug the x-coordinate back into the original function.
The point is then .
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