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Optimization problem with graph

  1. Nov 27, 2007 #1
    1. The problem statement, all variables and given/known data
    We are given a graph of gallons of fuel per hour versus miles per hour and asked what speed should be used to maximize fuel efficiency and also what is the optimal speed(are these two the same thing).

    2. Relevant equations
    I understand optimization using the first derivitive when given an equation, I am having a problem with figuring out what to do with only a graph

    3. The attempt at a solution

    I have graphed the first derivitive. should I use the zero points from the first derivitive graph to optimize the fuel efficiency?

    Thanks in advance.
  2. jcsd
  3. Nov 27, 2007 #2


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    Staff Emeritus
    Science Advisor

    "Optimal" simply means "best". IF "optimal" here means "best fuel efficiency", then they are the same.

    Yes, the max or min points will be where the first derivative is 0. I don't know that you really needed to graph the entire derivative. The derivative will be 0 where the original graph has a horizontal tangent.
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