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5.4. Convexity, concavity and inflection points

Lecture



Function graph   5.4.  Convexity, concavity and inflection points called convex in the interval   5.4.  Convexity, concavity and inflection points if it is located below the tangent held at any point of this interval.

Function graph   5.4.  Convexity, concavity and inflection points called concave in the interval   5.4.  Convexity, concavity and inflection points if it is located above the tangent held at any point in this interval.

Point function graph   5.4.  Convexity, concavity and inflection points , separating the convex part from the concave, is called the inflection point.

If a   5.4.  Convexity, concavity and inflection points in the interval   5.4.  Convexity, concavity and inflection points , the graph of the function on this interval is concave.

If a   5.4.  Convexity, concavity and inflection points in the interval   5.4.  Convexity, concavity and inflection points , then the graph of the function on this interval is convex.

If a   5.4.  Convexity, concavity and inflection points and when passing through the point x o the second derivative   5.4.  Convexity, concavity and inflection points changes the sign then the point of the graph   5.4.  Convexity, concavity and inflection points is a point of inflection; when examining a function, one should take into account points where the second derivative does not exist.


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Mathematical analysis. Differential calculus

Terms: Mathematical analysis. Differential calculus