If f(x) is concave down, then f”(x) is?
If f(x) is concave down, it means that the graph of the function is shaped like a downward-facing “U”
If f(x) is concave down, it means that the graph of the function is shaped like a downward-facing “U”. In other words, as you move from left to right along the graph, the curve is curving downward.
The concavity of a function is determined by its second derivative, f”(x). The second derivative tells us the rate at which the slope of the function is changing. To find the concavity of f(x), we need to determine whether f”(x) is positive or negative.
If f”(x) is positive, it means that the slope of the function is increasing, and the graph is concave up. This is the opposite of concave down.
If f”(x) is negative, it means that the slope of the function is decreasing, and the graph is concave down. This matches the initial given condition.
Therefore, if f(x) is concave down, then f”(x) is negative.
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