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Math Help - Linear approximation

  1. #1
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    Linear approximation

    The demand function for a product is given by

    p=f(q)=30 -q

    where p is the price per unit in dollars for q units. Use the linear approximation to approximate the the price when 224 units are demanded.
    Solution: We want to approximate f(224). From

    f(q) L(q)=f(a)+f(a)(q-a)

    and the fact that f(a)= a)-1/sqrt(a)
    b) 1/(2sqrt(a))
    c) - 1/(2sqrt(a))
    d) 1/sqrt(a)

    we choose a= ____________ .

    From f(225)= ________ and f(225)= ________ we get f(224) ______ .
    Hence, the price per unit when 224 units are demanded is approximately $ _________ .
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lemontea View Post
    The demand function for a product is given by

    p=f(q)=30 -q

    where p is the price per unit in dollars for q units. Use the linear approximation to approximate the the price when 224 units are demanded.
    Solution: We want to approximate f(224). From

    f(q) L(q)=f(a)+f(a)(q-a)

    and the fact that f(a)= a)-1/sqrt(a)
    b) 1/(2sqrt(a))
    c) - 1/(2sqrt(a))
    d) 1/sqrt(a)

    we choose a= ____________ .

    From f(225)= ________ and f(225)= ________ we get f(224) ______ .
    Hence, the price per unit when 224 units are demanded is approximately $ _________ .
    a = 225 of course. the second to last line kind of gave that away.

    f'(q) = \frac {-1}{2 \sqrt q} (we used the power rule here, recall that \sqrt q = q^{1/2})

    now just plug the values into the formula and calculate
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