If f'(x) is decreasing, then f”(x) is?
If \( f'(x) \) is decreasing, it means that the derivative of the function \( f(x) \) is decreasing
If \( f'(x) \) is decreasing, it means that the derivative of the function \( f(x) \) is decreasing.
To determine the behavior of \( f”(x) \), the second derivative of \( f(x) \), we can look at the rate of change of the derivative, or the slope of the derivative function.
If \( f'(x) \) is decreasing, it implies that the slope of the derivative function is decreasing. This means that the rate of change of the derivative is decreasing.
Now, the rate of change of the derivative is determined by the derivative of the derivative, \( f”(x) \). If the rate of change of the derivative is decreasing, it means that the slope of the second derivative function is negative (i.e., the second derivative is decreasing).
So, if \( f'(x) \) is decreasing, then \( f”(x) \) is also decreasing.
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