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 “going up” as x increases.
The derivative of a function, denoted as f'(x) or dy/dx, represents the rate at which the function is changing at a particular point. Intuitively, it gives us the slope of the function at that point.
If a function is increasing, it means that the slope of the function is positive. In other words, as x increases, the function is getting steeper in a positive direction. Therefore, the derivative f'(x) of an increasing function should be positive.
To summarize, if f(x) is increasing, then f'(x) is positive.
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