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. **

Metal can be embossed by using a process called die-cutting, where a metal sheet is placed on a die that has a raised design. The metal sheet is then pressed against the die using a hydraulic press, which creates the embossed design on the metal. Another method is to use embossing tools and a hammer to manually create the design on the metal surface. Additionally, metal can also be embossed using heat and pressure, where the metal is heated and then pressed against a die to create the embossed pattern. **

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. **

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. **

A local extremum is not necessarily a global extremum. A local extremum is a point where the function reaches a maximum or minimum value within a small neighborhood, but it may not be the highest or lowest point in the entire function. A global extremum, on the other hand, is the highest or lowest point in the entire function. Therefore, a local extremum may or may not be a global extremum, depending on the behavior of the function in the larger context. **