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

(1) Local Maximum: A local maximum is a point in a function where the value of that function at that specific point is greater than or equal to the values of the function at all nearby points. In other words, a point on the function is a local maximum if there exists some interval around that point such that for all points in this interval, the value of the function at the local maximum is greater. (2) Local Minimum: A local minimum is a point in a function where the value of that function at that point is less than or equal to the values of the function at all nearby points. In other words, a point on the function is a local minimum if there exists some interval around that point such that for all points in this interval, the value of the function at the local minimum is less. (3) Maximum: A maximum of a function is a point where the function reaches its highest value. In the entire domain of the function, the value at this point is greater than or equal to the value at every other point. If there exist more than one point with same highest value, then the function can have more than one maximum. (4) Minimum: A minimum of a function is a point where the function reaches its lowest value. Across the function's entire domain, the value at this point is less than or equal to the value at every other point. If there are more than one point with same lowest value, then the function can have more than one minimum.