The second derivative of the function (d²Y/dX² )is negative at the optimal solution of X=22.Therefore,we know that the solution X=22,where the first derivative equals zero… A)must be a minimum. B)must be a maximum. C)may be either a maximum or a minimum. D)would be nothing,because the second derivative is negative.

Question

Quizplus · Accepted Answer

A negative second derivative indicates that at the critical point (where the first derivative equals zero), the function is concave down. This means that the critical point is a local maximum if the first derivative changes from positive to negative at that point, or a local minimum if the first derivative changes from negative to positive. Since we know that the first derivative equals zero at X=22, and the second derivative is negative, we can conclude that X=22 is a local minimum. Therefore, the best choice is (A) that X=22 must be a minimum.

The Second Derivative of the Function (D2Y/dX2 )Is Negative at the Optimal

The Second Derivative of the Function (D²Y/dX² )Is Negative at the Optimal