Inflection Points
To understand inflection points it is important to be able to distinguish between concave and convex funcitons. A concave function is a function where no line the joins two points on it goes above the graph. A convex function is the opposite (imply below).It is also important to know what a root is: where the function equals zero.
Before you can find an inflection point you must first find the derivative of the function being graphed.
Find the second derivative (derivative of first derivative) and set it equal to zero.
Your answer will be a possible inflection point.
Find the third derivative of the function to determine whether or not the possible inflection point is truly an inflection point or not. If the answer does not equal zero then it is an inflection point.
To find the coordinates of the inflection point (x, F(x)) calculate the function based on the value of x (which will have been determined earlier in the process).
Plot the coordinates and your inflection point has been found.
Nice and clear!
ReplyDeletebaxter,
ReplyDeletei like how you introduced this lesson by discussing the concepts of concave and convex. some images and examples would have added a little bit more to this lesson, but you did provide good information about the meaning of inflection points.
professor little