5.4. Convexity, concavity and inflection points

Function graph called convex in the interval if it is located below the tangent held at any point of this interval.

Function graph called concave in the interval if it is located above the tangent held at any point in this interval.

Point function graph , separating the convex part from the concave, is called the inflection point.

If a in the interval , the graph of the function on this interval is concave.

If a in the interval , then the graph of the function on this interval is convex.

If a and when passing through the point x _{o the} second derivative changes the sign then the point of the graph is a point of inflection; when examining a function, one should take into account points where the second derivative does not exist.