Question

When there's a local maximum at (1/2,2) for the function (,)=+/+/+ (where and are both greater than 0), what type of extremum is it, and what is the value of the function at this point?

Answer 1

The local maximum is a relative maximum and the value of the function at this point is 2.

Step-by-step explanation:

A local maximum occurs when the function reaches a high point in a specific interval. In this case, we have a local maximum at (1/2, 2) for the given function. To determine the type of extremum at this point, we need to consider the concavity of the function. Since the second derivative is positive, this means the function is concave up and the local maximum is a relative maximum. The value of the function at this point is 2.