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. **

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. **

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. **

A sharpening function is a digital image processing technique used to enhance the edges and details in an image. It works by increasing the contrast along the edges to make them appear sharper and more defined. This process can help improve the overall clarity and quality of an image by making it appear more crisp and detailed. Sharpening functions are commonly used in photography and graphic design to enhance the visual impact of an image. **

Sharpening the chain refers to the process of filing the cutting teeth on a chainsaw chain to ensure they are sharp and able to cut efficiently. Over time, the cutting teeth can become dull from use, which can result in slower cutting speeds and a higher risk of kickback. Regularly sharpening the chain helps maintain its cutting performance and prolongs its lifespan. **

No, a local extremum is not necessarily a global extremum. A local extremum is a point where a function reaches a maximum or minimum value within a small neighborhood, while a global extremum is the absolute maximum or minimum value of the function over its entire domain. A local extremum may or may not be the global extremum depending on the behavior of the function in the rest of the domain. **

Local extrema are determined by finding critical points where the derivative of the function is zero or undefined, and then using the first or second derivative test to determine if the critical point is a local maximum or minimum. Global extrema are found by comparing the values of the function at the critical points, endpoints of the interval, and any other relevant points within the interval. The highest value among these points is the global maximum, and the lowest value is the global minimum. **