If f(x) is concave up, then f”(x) is?
If f(x) is concave up, it means that the graph of the function is shaped like a bowl, opening upwards
If f(x) is concave up, it means that the graph of the function is shaped like a bowl, opening upwards. In other words, as you move from left to right along the graph, the function is curving upwards.
The second derivative of a function, f”(x), tells us about the concavity of the function. If f”(x) is positive, it means that the graph of the function is concave up. If f”(x) is negative, it means that the graph of the function is concave down, like a bowl opening downwards.
Therefore, if f(x) is concave up, we can conclude that f”(x) is positive. The positive second derivative indicates that the rate of change of the slope (or the curvature) of the function is increasing as we move from left to right along the graph.
It’s important to note that while a positive second derivative implies concave up, a concave up function does not necessarily have a positive second derivative. There could be points on the graph where the second derivative is zero or undefined, which are the points where the concavity can change.
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