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Fermat’s theorem The connection between local extrema (maximum and minimum points) of a function and its derivative is captured by Fermat's theorem, which states that at any local extremum, the derivative of the function is zero. This means that the slope of the tangent line to the curve at these points is horizontal. While a zero derivative is necessary for a local extremum, it's not always sufficient; further analysis, often using the first or second derivative tests, is required to confirm wh
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