If f(x) is concave up, then f”(x) is?
If a function f(x) is concave up, it means that the graph of the function is curving upwards
If a function f(x) is concave up, it means that the graph of the function is curving upwards. In other words, as you move from left to right along the graph, the slope of the function is increasing.
The second derivative of a function, denoted as f”(x), represents the rate of change of the first derivative, or the slope of the tangent line to the graph of f(x). When f”(x) is positive, it means that the slope of the tangent line is increasing as x increases.
Since f(x) is concave up, this means that the slope of the tangent line is increasing as x increases. This implies that f”(x) is positive. Therefore, if f(x) is concave up, then f”(x) is positive.
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