if f'(x) is GREATER than 0, then f is _____ on (a,b)
If f'(x) is greater than 0 on the interval (a,b), it means that the derivative of the function f(x) is positive for all points within the interval (a,b)
If f'(x) is greater than 0 on the interval (a,b), it means that the derivative of the function f(x) is positive for all points within the interval (a,b). This indicates that the function is increasing on the interval.
In other words, if f'(x) > 0 for all x in (a,b), then f(x) is increasing on (a,b). This means that as the values of x increase within the interval, the corresponding values of f(x) also increase.
It is important to note that this definition holds for open intervals (a,b), where a and b are real numbers. If the interval is closed, i.e., [a,b], then the statement would be slightly different. In that case, “f is non-decreasing” would be a more accurate description, as f(x) could be constant at certain points within the interval.
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