No, not all global extremum points are also local extremum points of polynomial functions. Global extremum points are the highest or lowest points on the entire function, while local extremum points are the highest or lowest points within a specific interval. A polynomial function can have global extremum points that are not local extremum points if the function continues to increase or decrease beyond the local extremum point. **

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. **

To calculate the local maximum and minimum points of a function, you first find the critical points by taking the derivative of the function and setting it equal to zero. Then, you use the second derivative test to determine whether each critical point is a local maximum, local minimum, or neither. If the second derivative is positive at a critical point, it is a local minimum, and if the second derivative is negative, it is a local maximum. If the second derivative is zero, the test is inconclusive and you may need to use other methods to determine the nature of the critical point. **

Yes, a third-degree function can have two local maximum points. A third-degree function is a polynomial function of the form f(x) = ax^3 + bx^2 + cx + d, and it can have up to two local maximum or minimum points. The number and location of the local maximum and minimum points depend on the values of the coefficients a, b, and c. If the coefficients are such that the function has two local maximum points, then it is possible for a third-degree function to have two local maximum points. **

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Critical points are points on a graph where the derivative of a function is either zero or undefined. They are important because they can indicate where a function reaches a maximum, minimum, or a point of inflection. Inflection points, on the other hand, are points on a graph where the concavity changes. At an inflection point, the second derivative of the function is zero or undefined. **