f(x) is concave down when f’ is ____ or f” is ____
decreasing, f” < 0
To determine whether f(x) is concave down, we can look at the second derivative of the function, denoted as f”(x). If f”(x) is negative, then the function is concave down.
Alternatively, we can look at the first derivative of the function, denoted as f'(x), and check if its slope is decreasing as we move from left to right. If it is decreasing, then the function is concave down.
Therefore, f(x) is concave down when f’ is decreasing, or f” is negative.
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