If f(x) is increasing, then f'(x) is?
If f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase
If f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase. In other words, the function is getting “steeper” as x increases.
The derivative of a function, denoted as f'(x), represents the rate of change of the function at any given point.
If f(x) is increasing, it means that its slope is positive at every point, because the function is getting steeper as x increases. In terms of the derivative, this implies that f'(x) is positive for every x.
Therefore, if f(x) is increasing, then f'(x) is positive.
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