1. Sketch a graph on the axes below of a function $f(x)$ that satisfies the following requirements:$\bigskip $

      1. The domain is $[-4,4].\bigskip $

      2. $f~^{\prime }(x)<0$ for all $x.\bigskip $

      3. The function has an inflection point at MATH
        MATH
        $\bigskip $

  2. Find the equation of the line tangent to the curve $xy=y^{2}-12x$ at the point MATH
    MATH
    $\pagebreak $

  3. If a rectangle has a perimeter of 100 feet, what is the largest area it can have, assuming that the height and the width must be at least 1 foot each? $\ $(Hint: $\ $Start by expressing the area as a function of the width of the rectangle.)
    MATH

  4. A particular box has a square base. If its width is \underline{increasing} at a rate of 2 cm/sec and its height is \underline{decreasing} at a rate of 3 cm/sec, how fast is its volume changing when the width is 5 cm and the height is 4 cm?
    MATH

  5. Short answer.$\bigskip $

    1. Let MATH Find MATH
      MATH
      $\bigskip $

    2. Let $y=x^{2}-3$. Let $x=4$ and let $dx=0.2$. Find $dy$ and $\triangle y$. (Make sure to clearly label each.)$\bigskip $
      MATH
      $\bigskip $

  6. Short answer.$\bigskip $

    1. If $g(x)=f(x^{2}),$ find MATH in terms of $f~^{\prime },$ and MATH
      MATH
      $\bigskip $

    2. For the graph below, state all local and absolute maxima and minima and where they occur.$\bigskip \bigskip $
      MATH

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