اختبار تحدّب وتقعّر الدالة ... Concavity and Convexity Test

يشرح هذا المقطع بالأمثلة الرياضياتية اختبار تحدّب وتقعّر الدالة ... Test of Concavity & Convexity of a function. #test

In #calculus, the #concavity and #convexity of a function refers to the shape of the function's graph. Concavity refers to the degree to which a function curves upward or downward, while convexity refers to the degree to which it curves outward or inward.

To test for concavity and convexity, we can use the second derivative test. The second derivative of a function gives us information about the curvature of the function.

If the second derivative of a function is positive at a point, then the function is concave upward at that point. This means that the function is curving upward and becoming steeper.

If the second derivative is negative at a point, then the function is concave downward at that point. This means that the function is curving downward and becoming flatter.

If the second derivative is zero at a point, then the test is inconclusive and we need to use other methods to determine the concavity.

To test for convexity, we can look at the sign of the second derivative. If the second derivative is positive, then the function is convex. If it is negative, then the function is concave.

The concavity and convexity of a function are important because they tell us about the behavior of the function. Functions that are concave upward are often used to model increasing returns, while functions that are concave downward are often used to model decreasing returns. Functions that are convex are often used to model utility functions, where more is always better.