When f ‘(x) changes fro positive to negative, f(x) has a
When the derivative, f'(x), changes from positive to negative, it indicates that the function, f(x), is transitioning from increasing to decreasing
When the derivative, f'(x), changes from positive to negative, it indicates that the function, f(x), is transitioning from increasing to decreasing. In other words, the slope of the function at that particular point is changing from positive to negative.
This change in behavior can be observed on the graph of f(x) as a turning point, also known as a local maximum. At this point, the function reaches its highest value in a small interval surrounding it and starts to decrease afterward.
Mathematically, the turning point occurs at the x-coordinate where f'(x) changes from positive to negative. To determine the actual value of this turning point, we need to find the x-coordinate where f'(x) changes sign. This can be done by setting f'(x) equal to zero and solving for x.
Once the x-coordinate of the turning point is found, substitute it into the original function f(x) to obtain the corresponding y-coordinate or the maximum value of the function.
More Answers:
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Understanding the Relationship Between the Derivative Function and the Slope of the Original Function