Identifier: Evaluating a Derivative

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.

–          $f‘\left(3\right)=$

–          ${\frac{\mathit{dy}}{\mathit{dx}}|}_{x=3}=$

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 $f\left(x\right)$ at x = 3 .

–          Determine the slope of the tangent line to $f\left(x\right)$ at x = 3 .