Below you will find an applet that animates what is is happening in this example.  The red line segments represent the gutter.  The yellow rectangle represents the cross sectional area.  Drag the green point to change the dimensions of the gutter.  As you do this, to the left, you will see a blue point tracing out the graph of the cross sectional area as a function of the value of x (or the height).  You can start the trace over by clicking on the red x in the lower right-hand corner of the applet.

  1. For what value of x does one find the maximum cross sectional area?
  2. What is the maximum cross sectional area?
  3. What is the equation of the parabola traced by the blue point?

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This is a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).