When f ‘(x) changes from negative to positive, f(x) has a
When the derivative, f'(x), changes from negative to positive, it indicates that the function f(x) is increasing at that particular point of x
When the derivative, f'(x), changes from negative to positive, it indicates that the function f(x) is increasing at that particular point of x.
To understand this, let’s break it down:
– The derivative of a function, f'(x), represents the rate of change of the function at a specific point. It tells us whether the function is decreasing, increasing, or neither at that point.
– If the derivative changes from negative to positive at a specific x value, it means that the function is transitioning from decreasing to increasing at that point.
– The notation f'(x) < 0 means that the function slope is negative at a particular x value, indicating a decreasing trend. Conversely, when f'(x) > 0, it represents that the function slope is positive, suggesting an increasing trend.
Therefore, when f ‘(x) changes from negative to positive, it means that the function f(x) is transitioning from a decreasing trend to an increasing trend at that specific x value.
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