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Math Help - function problem

  1. #1
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    function problem

    Hi, I have a function question may you help me?

    Which one is increasing function for all x values?
    (a) y = |x - 7|
    (b) y = 2x^2 + 9
    (c) 3x^3 -11
    (d) 4x^4 + 2 how can i prove?

    Thank you
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  2. #2
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    Re: function problem

    C (although it is neither increasing nor decreasing at x = 0)

    All the other ones are decreasing for part of the domain.
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  3. #3
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    Re: function problem

    Quote Originally Posted by sunrise View Post
    Hi, I have a function question may you help me?
    Which one is increasing function for all x values?
    (a) y = |x - 7|
    (b) y = 2x^2 + 9
    (c) 3x^3 -11
    (d) 4x^4 + 2 how can i prove?
    You posted this in the pre-calculus forum.
    Thus there is no way to prove this one way or the other.
    You can simply draw the graphs and see the answer. But that is hardly a poof.

    On the other hand, with calculus we can see which one has a non-negative derivative. That would prove it.
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  4. #4
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    Re: function problem

    richard,
    How you solved and thought that C is increasing?
    Should i give value to the x?
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  5. #5
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    Re: function problem

    Quote Originally Posted by sunrise View Post
    richard,
    How you solved and thought that C is increasing?
    Should i give value to the x?
    Assigning a value to x has no indication of whether a function is increasing or not.

    Why don't you just graph the function? To rigorously prove it, we note that its derivative is 9x^2, which is always non-negative. Therefore the function in (C) is always increasing (except when x = 0, where the derivative is zero).
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  6. #6
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    Re: function problem

    Quote Originally Posted by richard1234 View Post
    (C) is always increasing (except when x = 0, where the derivative is zero).
    Technically the function f(x)=3x^3-11 is increasing everywhere.

    The the statement that f is an increasing function means that if a<b then f(a)<f(b).

    That is clearly true in this case. When I made the remark reply #3 about proof, it was addressing the fact that this is a precalculus forum.
    There is of course a perfectly good way of proving this.

    Suppose that a<b then a^3<b^3 then a^3-11<b^3-11. Proved.
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  7. #7
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    Re: function problem

    If we think from your idea,

    y = 2x^2 + 9 is also increasing isnt it?

    Thanks
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  8. #8
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    Re: function problem

    Quote Originally Posted by sunrise View Post
    If we think from your idea,
    f(x) = 2x^2 + 9 is also increasing isnt it?
    No it is not.
    -3<1 BUT f(-3)>f(1).
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  9. #9
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    Re: function problem

    Now I understand thank you.
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