Geometry-tangent-lines.tex

\Section{Geometry---tangent lines}

Let's work with the following function.
\begin{equation*}
 f(x) = - \frac{1}{2} x^2 + 3x + 5
\end{equation*}
\begin{ProblemSet}
 \begin{Problem}
  There is one point on the graph of $f$ at which $x = -2$.
  Write this point as an ordered pair.
 \end{Problem}
 \begin{Problem}
  What is the derivative of $f$?
 \end{Problem}
 \begin{Problem}
  What is the instantaneous rate of change of $f$ with respect to $x$ at $x = -2$?
 \end{Problem}
 \begin{Problem}
  What is the slope of the line tangent to the graph of $f$ at $x = -2$?
 \end{Problem}
 \begin{Problem}[pencil space=2.5in]
  Write an equation of the line tangent to the graph of $f$ at $x = -2$.
 \end{Problem}
 \begin{Problem}
  On the grid below, sketch the graph of $f$.
  Use your calculator to help.
  Use $\xMin = -10$, $\xMax = 10$, $\yMin = -30$, $\yMax = 30$.
  Then draw the line tangent to the graph of $f$ at $x = -2$.

  \bigskip
  \GraphingGridMedium
 \end{Problem}
\end{ProblemSet}

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