When f ‘(x) changes from negative to positive, f(x) has a
When f ‘(x) changes from negative to positive, it means that the derivative of the function f(x) is initially negative and then becomes positive
When f ‘(x) changes from negative to positive, it means that the derivative of the function f(x) is initially negative and then becomes positive. This indicates a change in the slope of the function at that point.
The function f(x) represents the rate of change of another function, which is known as the derivative. When f ‘(x) changes from negative to positive, it suggests that the slope of the original function is initially decreasing and then starts increasing.
In terms of the behavior of f(x), if f ‘(x) changes from negative to positive at a specific point, it means that the function f(x) changes from having a decreasing slope to having an increasing slope at that point.
Mathematically, this can be seen as a change from a decreasing interval to an increasing interval for the function f(x). It could also signify a change from a concave down (where f ”(x) < 0) interval to a concave up (where f ''(x) > 0) interval.
It is important to note that identifying when f ‘(x) changes from negative to positive can help locate critical points, minimum or maximum points, or inflection points in a mathematical function. This information can provide insights into the behavior and properties of the function.
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