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Math Help - optimazation problem

  1. #1
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    optimazation problem

    a model for the us average price of a pound of white sugar from 1993 to 2003 is given by the function S(t)= -0.00003237t^5 + 0.0009037t^4 -0.008956t^3 + 0.03629t^2 + 0.4074 where t is measured in years since August of 1993. estimate the times which sugar was cheapest and most expensive during the decade from 1993 to 2003,

    I know i need to take the derivative and find the critical points but i am having a hard time setting the derivative to zero
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by flashdawg View Post
    a model for the us average price of a pound of white sugar from 1993 to 2003 is given by the function S(t)= -0.00003237t^5 + 0.0009037t^4 -0.008956t^3 + 0.03629t^2 + 0.4074 where t is measured in years since August of 1993. estimate the times which sugar was cheapest and most expensive during the decade from 1993 to 2003,

    I know i need to take the derivative and find the critical points but i am having a hard time setting the derivative to zero

    The maximum (minimum) of a function on an interval will be a calculus type extremum in the interval or occur at an end point of the interval.

    What do you have for the derivative?

    You will notice that t=0 is one root, so take out t to leave you with a cubic. Plot the cubic to see where ther roots if any are between 0 and 10, you may find that there are no further roots in the given range.

    So you have a calculus like extremum at t=0, and there will be another maximum or minimum at the other end of the interval.

    So calculate S(0) and S(10) the smaller will be the global minimum of S in the interval and the larger will be the global maximum in the interval.

    Finally you might just as well have plotted S(t) for t between 0 and 10 anyway.

    CB
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