Ask AI: Suppose f is a function of f(a)=f(b), define the following, (1)local maximum (2) local minimum (3) maximum (4) minimum

Sure, I'll be happy to explain these terms for you: 1) Local Maximum: A local maximum of a function is a point where the function's value is greater than or equal to the values of all other points in a local region around that point. In other words, in a small interval around the point, the function obtains a maximum value. But another point outside this local interval may have a higher value compared to this local maximum. 2) Local Minimum: This is the point in the function where a value is less than or equal to the values of all other points in the nearby area. So in a small interval around that point, the function obtains a minimum value. There could be other points beyond this local neighborhood where the function has a smaller value than this local minimum. 3) Maximum: This is the point where the function reaches its highest value. In the entire domain of the function, this value is the maximum. It is also known as the absolute or global maximum. 4) Minimum: This is the point where the function reaches its lowest value. This value is the absolute or global minimum when compared to all other values of the function in the entire domain it is defined. Note: In all cases, a function may have multiple local maxima or minima and the function may not necessarily have global maxima or minima depending on its definition and domain.