Understanding Derivatives, Relative Extrema, and Points of Inflection
The Big Idea When studying a function, we often want to answer three important questions: Is the function increasing or decreasing? Does the function have any local maxima or minima? Where does the graph change its shape or curvature? These questions can be answered using the first and second derivatives. The first derivative helps us…
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Why the Limit Does Not Care About the Function Value
Common Misconception Many students think that to find a limit, we simply use the function value. This is not always true. A limit looks at what happens near a point, not necessarily at the point. Example Suppose: 
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Limit Value vs Function Value
The Big Idea A limit value and a function value are two different concepts. The limit tells us what value the function is approaching. The function value tells us the actual value of the function at a specific point. Therefore, the limit can exist even if the function value is different or does not exist.…
