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Math Help - max/min problems

  1. #1
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    max/min problems

    I'm at my wits end with my Calculus homework. I have a test tomorrow and I must have an 80% on every assignment or I will be unable to take the test. I'm done with a lot of it but at this point my brain is mush and I hit a brick wall with every problem or am unable to even set up the problems to begin with.

    1. Find two positive numbers whose product is 218 and whose sum is a minimum. (Give your answer correct to 2 decimal places.)
    ___ (smaller number)
    ___ (larger number)

    2. Consider the function below.
    Find the point on the graph of function that is closest to the point (-3, 12).
    ___

    3. On a given day, the flow rate F (in cars per hour) on a congested roadway is given by the equation below, where v is the speed of traffic in miles per hour.
    What speed will maximize the flow rate on the road? (Give your answer correct to 1 decimal place.)
    ___ mph

    4. Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 343.5 square centimeters. (Give your answer correct to 2 decimal places.)
    ___ cm (length)
    ___ cm (width)
    ___ cm (height)

    5. An offshore oil rig well is 1 kilometers off the coast. The refinery is 5 kilometers down the coast. Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost? Complete the following statement. (Give your answer correct to 2 decimal places.)

    The pipe should be laid in the ocean from the rig to a point on the coast ______ km from the refinery, then on land the remainder of the distance to the refinery.

    Any help would be appreciated.
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by thebacontalks2me View Post
    I'm at my wits end with my Calculus homework. I have a test tomorrow and I must have an 80% on every assignment or I will be unable to take the test. I'm done with a lot of it but at this point my brain is mush and I hit a brick wall with every problem or am unable to even set up the problems to begin with.

    1. Find two positive numbers whose product is 218 and whose sum is a minimum. (Give your answer correct to 2 decimal places.)
    ___ (smaller number)
    ___ (larger number)

    This is your entire problem set?
    I will give you a hand with the first problem for now. Let the numbers be x and y. The product xy = 218, which means y = \frac{218}{x}.
    The sum (to be optimized) is A = x + y = x + \frac{218}{x}

    Find the first derivative \frac{dA}{dx} , then solve for the critical numbers by setting the derivative equal to zero or undefined. Use the first OR second derivative test to convince yourself or justify that it is a minimum.

    Good luck!!
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  3. #3
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    Yeah I knew that one was really easy but I was never shown how to do it.

    This may be against forum rules but if someone will talk me through these problems via online chat. I will compensate them for tutoring me.
    Last edited by thebacontalks2me; April 15th 2009 at 06:17 PM.
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  4. #4
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    Quote Originally Posted by thebacontalks2me View Post
    [snip]
    2. Consider the function below.
    Find the point on the graph of function that is closest to the point (-3, 12).
    ___

    [snip]
    You asked this question here and got replies: http://www.mathhelpforum.com/math-he...e-problem.html
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