Related Rates Discussion

This discussion gives you a chance to start working hands-on with related rates problems. See section 4.1 in our textbook for a description and examples of these problems. In particular, the “Setting Up Related-Rates Problems” subsection introduces the basic style of problem and solution method.

Start with the following example. I’ll post another example when this one is done, e.g., when we have a solution and explanation of it, or key questions that get answered, etc. Then I’ll post another, and so forth until between the discussion and class meetings we’ve covered the topic.

So, to get started.... Most computer drawing programs let you draw squares and rectangles by dragging one corner of the shape, thus changing the height and width simultaneously (for an example in Word, open a blank document; go to the “Insert” menu, then “Shape -> Rectangle.” Click somewhere in your document and drag; a rectangle will appear and grow to follow your cursor). Suppose you’re drawing a square with such a tool, doing it in such a way that the height and width are both changing at a rate of 2 cm/sec. How fast is the area changing when the sides are both 5 cm long?