In this context, $x = k$ represents a specific value of $x$ where we want to analyze what happens in relation to the given conditions.
Think of $x = k$ as marking a particular spot on your journey where you want to examine what's happening around that location without considering previous or subsequent locations.
Domain: The domain of a function consists of all possible input values (usually represented by $x$) for which the function is defined.
Range: The range of a function consists of all possible output values (usually represented by $y$) that can be obtained from plugging in different inputs.
Critical value: A critical value occurs when either the first derivative equals zero or does not exist. These points are important for analyzing functions and finding extrema or inflection points.
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