There are several ways you can be asked to evaluate a derivative at a single point.
i) Notation
All of these notations mean the same thing when you see them, find the derivative and evaluate it (plug in a value) at x = 3.
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ii) Language
You can be asked to evaluate the derivative using language. All of this language is saying the same thing, find the derivative and evaluate it (plug in a value) at x = 3 .
– Determine the instantaneous rate of change of at x = 3 .
– Determine the slope of the tangent line to at x = 3 .