If f(x) is decreasing, it means that as x increases, the value of f(x) decreases. This implies that the slope of the function is negative for all values of x.
In calculus, the slope of a function is represented by its derivative. Therefore, if f(x) is decreasing, it follows that its derivative, f'(x), is negative for all x.
In summary, if a function f(x) is decreasing, its derivative f'(x) is negative for all x.
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