Points of Inflection -

Points of inflection (or inflection points) can be points on a curve in which the curvature (or concavity) of the curve changes. This point also corrisponds to the point where a line tangent to that curve intersects the curve.

On a function, the points of inflection is a point on a function **f(x)**, where **f'(x) **is at an extremum. *

*Note: The lowest non-zero derivative of the function must be an odd order in order for those points to be points of inflection (1st, 3rd, 5th, etc..)

Points of inflection are where a change occurs in the rate at which the function changes.

EXAMPLE:

If you throw a ball directly upward, and you graphed position as **f(x), **velocity as **f'(x)**, and acceleration as **f"(x)**. At the point where the ball is farthest from the ground, the position is switching direction. *CONTINUE HERE*

Concavity -

Andrew Stanford

PAGES TO SITE FROM:

http://en.wikipedia.org/wiki/Inflection_point

http://www.sosmath.com/calculus/diff/der15/der15.html

http://library.thinkquest.org/3616/Calc/S2/FCPoI.html

http://en.wikipedia.org/wiki/Curvature

## Comments (1)

## Anonymous said

at 8:55 am on Feb 21, 2008

Well, the page is incomplete...doesn't have the required elements...etc. etc. Please complete it! Mr. S

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