Theorem 3 is no help here, since the interval for this problem is 0 < x < 1. The problem is fairly simple -- you shouldn't need to invoke a theorem to answer it.Karol said:
Karol said:
Karol said:
Karol said:
A maximum value is the largest value that a function or data set can take on within a given range. A minimum value is the smallest value that a function or data set can take on within a given range.
To find the maximum and minimum values of a function, you can use calculus techniques such as taking the derivative and setting it equal to 0 to find critical points. Then, you can evaluate the function at these points to determine the maximum and minimum values.
An absolute maximum or minimum value is the largest or smallest value of a function over its entire domain. A local maximum or minimum value is the largest or smallest value of a function within a specific interval or region.
A function is continuous if it has no breaks or jumps in its graph. This means that the function can be drawn without lifting the pen from the paper, and there are no sudden changes in the output values as the input values change.
A function is continuous at a specific point if the limit of the function as the input approaches that point is equal to the output value at that point. In other words, the left and right limits of the function at that point must exist and be equal to the function value at that point.