If f(x) is increasing, then f'(x) is?
If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase
If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase. In other words, the function slopes upward as you move from left to right on the graph.
The derivative of a function f'(x) measures the rate of change of the function f(x) at any given point x. In simpler terms, it tells us the slope of the function at a particular point.
Therefore, if f(x) is increasing, it implies that the slope of the function at each point is positive. Hence, f'(x) must be positive for every value of x. This means that the derivative f'(x) is greater than zero or strictly positive.
In summary, if a function f(x) is increasing, the derivative f'(x) will be positive.
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