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# Points of inflection as places where concavity changes

last edited by 15 years ago
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 