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.
More Answers:
Understanding the Instantaneous Rate of Change at a Specific Point: A Guide to Calculating the Derivative and Analyzing Function BehaviorUnderstanding the Relationship between Increasing Functions and Positive Derivatives in Mathematics.
Understanding the Relationship between the Decreasing Behavior of a Function and its Derivative
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