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 has a positive slope.
The derivative of a function, represented as f'(x), gives us the rate at which the function is changing at any given point. It tells us how much the function is increasing or decreasing as x changes by a small amount.
If f(x) is increasing, it means that the function has a positive slope. The derivative, f'(x), represents the slope of the function. Therefore, if f(x) is increasing, we expect f'(x) to be positive.
In mathematical terms, if f(x) is increasing, we can say that f'(x) > 0. This means that the derivative of the function at any given point is positive, indicating an increasing trend.
To summarize, if f(x) is increasing, then f'(x) is positive.
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