If f'(x) is decreasing, then f”(x) is?
If f'(x) is decreasing, it means that the slope of the graph of f(x) is becoming less and less steep as x increases
If f'(x) is decreasing, it means that the slope of the graph of f(x) is becoming less and less steep as x increases. In other words, the rate of change of f(x) is decreasing.
Now, f”(x) represents the derivative of f'(x), which measures the rate at which the slope of the graph of f(x) is changing. In other words, f”(x) represents the rate of change of the rate of change of f(x).
If f'(x) is decreasing, it implies that f”(x) must be negative. This is because a decreasing function has a negative derivative. Since f”(x) measures the rate of change of f'(x), a negative value for f”(x) indicates that the rate at which the slope of the graph of f(x) is changing is decreasing.
In summary, if f'(x) is decreasing, then f”(x) is negative, indicating that the rate of change of the rate of change of f(x) is decreasing.
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