Related Rates

1
Related Rates

• 4.6

2
Steps for Solving Related Rates Problems

• Carefully read the problem.
• Draw a diagram, if possible.
• Define the variables and state the givens in
  terms of those variables and there derivatives
  with respect to time.

3
Steps for Solving Related Rates Problems

• Write an equation that relates the variables in
  the problem.
• Use substitution to eliminate a variable if there
  is not enough information for all of the
  variables, or if it makes the problem easier.
• Watch for constants that simplify the equation.
• The equation should be able to answer the
  specific question asked.

4
Steps for Solving Related Rates Problems

• Use the chain rule to differentiate the equation
  with respect to t.
• Substitute the given information into the final
  equation and solve.
• Watch the signs.
• Assign units to the answer.

5

• This site contains links to animated gifs that
  show related rate problems in real time. It
  gives the students a real sense of related rates.
  (This site also seems to be okay to use)
• http//mathdemos.gcsu.edu/mathdemos/relatedrates/r
  elatedratesgallery.html

6

• This site contains some sample related rate
  problems. Underneath each problem, you can click
  on a button that will take you to the worked out
  solution.
• http//oregonstate.edu/instruct/mth251/cq/Stage9/P
  ractice/ratesProblems.html

7

• This site contains a related rate tutorial. The
  student reads through the intro and answers
  multiple choice and free response questions as
  they go. (It looks like I would have to get
  permission here)
• http//people.hofstra.edu/Stefan_waner/RealWorld/t
  utorials/frames4_4.html