Question

If f '(x) > 0 for 3 < x < 10, then f is ________ on (3, 10).

1) increasing
2) decreasing
3) constant
4) cannot be determined

Answer 1

If the derivative f '(x) is greater than zero on the interval 3 < x < 10, then the function f is increasing on that interval.

Step-by-step explanation:

If f '(x) > 0 for 3 < x < 10, then f is increasing on (3, 10). This is based on the fact that the derivative of a function gives us the slope of the tangent to the function at any given point. If the derivative is positive, the slope of the tangent line is positive, which means that the function is increasing at that interval. This directly relates to the behavior of the functional as a derivative that is greater than zero indicates that the function's rate of change is positive, and thus the function f(x) is increasing in that specified range.