If f(x) is concave up, then f”(x) is?
If a function f(x) is concave up, it means that its graph is shaped like a U and opens upwards
If a function f(x) is concave up, it means that its graph is shaped like a U and opens upwards. In terms of calculus, this can be determined by the second derivative of the function, f”(x).
The second derivative, f”(x), represents the rate of change of the first derivative, f'(x). In other words, it tells us how the slope of the function is changing.
To determine the concavity of f(x), we examine the sign of f”(x). If f”(x) is positive, it means that the slope of f(x) is increasing, and therefore, the graph of f(x) is concave up.
Conversely, if f”(x) is negative, it means that the slope of f(x) is decreasing, and thus, the graph of f(x) is concave down.
In summary, if f(x) is concave up, then f”(x) is positive.
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