Predetermined breaking points are specific levels or thresholds that are established in advance to indicate when a certain event or action should occur. These points are often used in financial markets to trigger automatic buying or selling of assets when the price reaches a certain level. Predetermined breaking points can help investors and traders manage risk and make decisions based on predetermined criteria rather than emotions. They are also used in other contexts, such as in project management, to indicate when a project is not meeting its goals and needs to be reevaluated or adjusted. **

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. **

Yes, headlines in a PowerPoint presentation are typically capitalized in English. This helps to make them stand out and easily catch the audience's attention. Bullet points, on the other hand, do not necessarily need to be capitalized, but it is a common practice to capitalize the first letter of each bullet point for consistency and readability. Ultimately, the decision to capitalize bullet points may depend on the specific style guide or preference of the presenter. **

Bonus points do not belong to regular points as they are typically earned through special promotions, offers, or specific actions. Regular points are usually earned through standard transactions or activities. Bonus points are often temporary and may have different redemption options or restrictions compared to regular points. **

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. **

Turning points are points on a curve where the direction of the curve changes, such as from increasing to decreasing or vice versa. These points can be local maxima or minima. Saddle points, on the other hand, are points on a surface where the surface curves upwards in some directions and downwards in others. At a saddle point, the surface is neither a maximum nor a minimum in any direction. Both turning points and saddle points are important in the study of calculus and optimization, as they help us understand the behavior of functions and surfaces. **

Points are deducted for i points in order to penalize a player for making a mistake or committing a foul. This deduction serves as a way to discourage undesirable behavior and to maintain fairness and sportsmanship in the game. By deducting points, it also encourages players to be more careful and strategic in their decisions, ultimately enhancing the overall competitiveness and integrity of the game. **