If f”(x) is > 0, then f”(x) is ___________ and f(x) is _____________.
If f”(x) is greater than zero, it means that the second derivative of the function f(x), denoted by f”(x), is positive
If f”(x) is greater than zero, it means that the second derivative of the function f(x), denoted by f”(x), is positive.
1. f”(x) is concave up: A positive second derivative implies that the graph of the function is concave up. Concave up means that the curve is shaped like a U, with the open side facing upward.
2. f(x) is increasing: Since f”(x) represents the rate of change of the first derivative f'(x), a positive second derivative means that the first derivative itself, f'(x), is increasing. Therefore, the function f(x) is getting steeper or sloping upwards, indicating that it is increasing in value as x increases.
In summary, if f”(x) is greater than zero, both f”(x) and f(x) exhibit characteristics of a graph that is concave up and increasing.
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