f'(x) changes from negative to positive
f(x) has a relative minimum
When f'(x) changes from negative to positive, it means that the slope of the graph of the function f(x) is changing from negative to positive. In other words, the function is changing from decreasing to increasing.
This occurs at a local minimum or a point of inflection, where the slope of the function changes direction. At this point, the rate of change of the function is zero, which means that the function has reached a turning point.
To find the point where f'(x) changes from negative to positive, you can take the derivative of the function and set it equal to zero to find the critical point. Then, you can evaluate the sign of f'(x) on either side of the critical point to see if it changes from negative to positive.
Alternatively, you can examine the graph of the function and observe where the slope changes from negative to positive. This point will be a minimum or a point of inflection.
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