If f(x) is decreasing, then f'(x) is?
If the function f(x) is decreasing, it means that as x increases, the corresponding values of f(x) decrease
If the function f(x) is decreasing, it means that as x increases, the corresponding values of f(x) decrease. In terms of calculus, this implies that the derivative of the function, f'(x), is negative.
Consider the definition of the derivative: f'(x) represents the rate of change of the function f(x) with respect to x. When f(x) is decreasing, it indicates that the function is becoming smaller as x increases. Therefore, the derivative f'(x) is negative because it represents the rate at which f(x) is decreasing.
Mathematically, if f(x) is a decreasing function, it can be expressed as f'(x) < 0 for all x in the domain of f(x). In summary, when a function f(x) is decreasing, its derivative f'(x) will be negative.
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