If f(x) is increasing, then f'(x) is?
If a function f(x) is increasing, it means that as the x-values increase, the corresponding y-values also increase
If a function f(x) is increasing, it means that as the x-values increase, the corresponding y-values also increase. In terms of calculus, this implies that the derivative of f(x), denoted as f'(x), is positive.
The derivative represents the rate of change of the function at any given point. If f(x) is increasing, it means that the slope of the tangent line at any point on the graph of f(x) is positive, indicating a positive rate of change.
Therefore, if f(x) is increasing, f'(x) is positive.
In mathematical notation, it can be stated as:
If f(x) is increasing, then f'(x) > 0.
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