Local minima and maxima refer to the points on a function where the function reaches a low or high point, respectively, within a small neighborhood of that point. Global minima and maxima, on the other hand, refer to the lowest and highest points on the entire function, respectively. In other words, global minima and maxima are the absolute lowest and highest points on the function, while local minima and maxima are only the lowest and highest points within a specific range. These concepts are important in optimization and calculus, as they help identify the best and worst points of a function. **

2 is a global maximum point if it is the largest value in the entire domain of the function. However, if there are other points in the domain that have a larger value than 2, then 2 would be considered a local maximum point. It ultimately depends on the specific function and its domain. **

Local extrema are points on a function where the function reaches a maximum or minimum value within a small neighborhood of that point. Global extrema, on the other hand, are points where the function reaches the maximum or minimum value over the entire domain of the function. Local extrema can occur at points where the derivative of the function is zero, while global extrema can occur at endpoints of the domain or at points where the derivative is zero. **

Local extrema are the highest or lowest points within a specific interval or region of a function. They can be either a local maximum (the highest point in the interval) or a local minimum (the lowest point in the interval). Global extrema, on the other hand, are the absolute highest or lowest points of the entire function, not just within a specific interval. These points represent the overall maximum or minimum values of the function. **

No, not all global extrema are also local extrema of polynomial functions. A global extremum is a point where the function has the highest or lowest value over its entire domain, while a local extremum is a point where the function has the highest or lowest value in a specific neighborhood. A polynomial function can have global extrema that are not local extrema if the function continues to increase or decrease beyond the neighborhood of the extremum. **

Global extreme points are the highest or lowest points in a function over its entire domain. They represent the absolute maximum or minimum values of the function. Local extreme points, on the other hand, are the highest or lowest points within a specific interval or neighborhood of a function. They represent the maximum or minimum values within a smaller range, but not necessarily the absolute maximum or minimum of the entire function. **

The set of divisors of 2 is {1, 2}. This is because a divisor of a number is a whole number that can be divided into the original number without leaving a remainder. In the case of 2, the only whole numbers that can divide into it without leaving a remainder are 1 and 2. Therefore, the set of divisors of 2 is {1, 2}. **

The global behavior of the function f(x) = 5x^2 is that it is a parabola that opens upwards. This means that as x increases or decreases, the function will continue to increase without bound. The function has a minimum value at the vertex, which is located at the point (0,0). As x approaches positive or negative infinity, the function will also approach positive infinity. Therefore, the global behavior of f(x) = 5x^2 is that it increases without bound as x increases or decreases. **