If f(x) is concave down, then f”(x) is?
f”(x) = negative
If f(x) is concave down, it means that the graph of f(x) is curving downward or bending towards the negative y-axis. This indicates that the slope of the graph is decreasing as we move along x-axis.
The second derivative of f(x), denoted as f”(x), represents the rate at which the slope of f(x) is changing. If f(x) is concave down, we know that the slope of the graph is decreasing, i.e., the rate of change of slope is negative. Mathematically, this can be represented as:
f”(x) < 0 Therefore, if f(x) is concave down, f''(x) must be negative or less than zero.
More Answers:
The Limit Definition Of Derivatives And Its Importance In CalculusMath: The Relationship Between Decreasing First Derivative And Negative Second Derivative
The Relationship Between Increasing F'(X) And Positive F”(X) – Exploring The Concave Up Graph Of F(X)
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