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Math Help - Function Inverse Help Please

  1. #1
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    Function Inverse Help Please

    Clovis is standing at the edge of a cliff, which slopes 6 feet downward from him for every 1 horizontal foot. He launches a small model rocket from where he is standing. With the origin of the coordinate system located where he is standing, and the x-axis extending horizontally, the path of the rocket is described by the formula y = −3x^2 + 120x.

    (a) Give a function h = f(x)
    relating the height h of the rocket above the sloping ground to its x-coordinate.
    -3x^2 + 126x
    (b) Find the maximum height of the rocket above the sloping ground. What is its x-coordinate when it is at its maximum height?
    1332, 121
    (c) Clovis measures its height h of the rocket above the sloping ground while it is going up. Give a function x = g(h)
    relating the x-coordinate of the rocket to h.

    How would I go about solving for c?
    Last edited by VARSOFFON; October 26th 2012 at 10:51 PM.
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  2. #2
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    Re: Function Inverse Help Please

    Hey VARSOFFON.

    With regards to part c, you want to find the region where the rocket is increasing which means that this will be from where it time = 0 to the time of the maximum.

    Hint: Consider completing the square and the take the right branch of the square root.
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  3. #3
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    Re: Function Inverse Help Please

    Ohh okay thank you very much!
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Function Inverse Help Please

    I think you mean for part b) the x-coordinate at the maximum height is 21, with a height of 1323.

    For part c), use:

    h(x)=-3x^2+126x where 0\le x\le21

    Now write this is standard quadratic form:

    3x^2-126x+h=0

    Use the quadratic formula, and take the root in the closed interval [0,21].
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