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Math Help - Calculus Question

  1. #1
    Member CalcGeek31's Avatar
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    Calculus Question

    A small plane is 34 miles east of an airport runway (at the origin) and starts to descend to the airport according to the formula h = -.00034x^3 +.0173 x^2 +.098x where h is the height of the plane and x is the distance of the plane from the runway. How far from the runway (to the nearest mile) would the plane be descending at the greatest rate?

    I started by taking the second derivative, and am not even sure if that is right, any help is appreciated.
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  2. #2
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    Quote Originally Posted by CalcGeek31 View Post
    A small plane is 34 miles east of an airport runway (at the origin) and starts to descend to the airport according to the formula h = -.00034x^3 +.0173 x^2 +.098x where h is the height of the plane and x is the distance of the plane from the runway. How far from the runway (to the nearest mile) would the plane be descending at the greatest rate?

    I started by taking the second derivative, and am not even sure if that is right, any help is appreciated.
    You want the greatest negative rate - in other words, the LEAST rate.

    So you want to find the minimum rate.

    Take the second derivative and set it equal to 0 to find the maximum and minimum rates.

    Suppose you get a minimum rate at x = a. Take the third derivative and check it's sign at x = a. If h'''(a) > 0 you have a minimum.
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  3. #3
    Member CalcGeek31's Avatar
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    then would i plug that value into the original equation?
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