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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 10}\quad {\sl Dec.\ 8, 1994}

\begin{enumerate}

\problemspace

\item A particle is constrained to move along a
  parabola whose equation is $y = x^2$.

  \begin{enumerate}[a)]

  \item At what point on the curve are the x-coordinate and the
  y-coordinate changing at the same rate.
  \answerspace

  \item  Find this rate if the motion is such that at time $t$ we have
  $x = \sin(t)$ and $y = \sin^2(t)$.
  \answerspace
    
  \end{enumerate}


\problemspace

\item Find the extrema of the function
$f(x) = 3x^4 + 4x^3 - 12x^2 + 1$ on the interval $[-3,2]$.
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\item 

  \begin{enumerate}[a)]

  \item State the \textsc{Mean Value Theorem for Derivatives}.
  \answerspace

  \item Use the \textsc{Mean Value Theorem} and \textsc{Bolzano's
  Theorem} to prove that the polynomial $f(x) = 2x^5 - 5x^2 + 1$ has
  exactly one root in the interval $[0,1]$.
  \answerspace

  \end{enumerate}


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