Local extrema are points on a graph where a function reaches a maximum or minimum value within a specific interval. A local maximum is the highest point in a small neighborhood of a function, while a local minimum is the lowest point in that neighborhood. These points are called "local" because they may not be the absolute highest or lowest points of the entire function, but rather within a limited range. **

Local extrema are the highest or lowest points within a specific interval or neighborhood of a function, while global extrema are the highest or lowest points of the entire function. In other words, local extrema are relative to a specific region of the function, while global extrema are absolute and apply to the entire function. Local extrema can occur at points where the derivative of the function is zero or undefined, while global extrema occur at the endpoints of the interval or at critical points within the interval. **

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. **

No, local extrema cannot be infinite. Local extrema refer to the maximum or minimum values of a function within a specific interval, and these values are finite. Infinite values would not qualify as local extrema because they do not represent a maximum or minimum within a specific range. **

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. **

To find local extrema in mathematics, you need to first find the critical points of the function by taking the derivative and setting it equal to zero. Then, you can 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 it is negative, it is a local maximum. **

To find local extrema in mathematics, one must first find the critical points of the function by taking the derivative and setting it equal to zero. Then, one can use the second derivative test to determine whether each critical point corresponds to a local maximum, local minimum, or neither. If the second derivative is positive at a critical point, it is a local minimum, and if it is negative, it is a local maximum. **