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Math Help - function g(x)=(1-2x)^2(x-3)

  1. #1
    Junior Member surffan's Avatar
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    function g(x)=(1-2x)^2(x-3)

    g(x)=(1-2x)^2(x-3)
    I need to state whether the function is odd or even and i said odd since there is a degree of 3, and the x and y intercepts i solved for and ended up with y=-2 and x=3,1/2. now i need to find the first and second derivative, and i was wondering if i should use the chain rule and product rule ?
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  2. #2
    Junior Member surffan's Avatar
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    I tried solving for the first derivative and i used the product rule and the chain rule
    g'(x)=(1-2x)^2 (1) + (2(-2)(1-2x)
    =(1-2x)^2 + -4(1-2x)
    =2x^2 +8x -3
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by surffan View Post
    g(x)=(1-2x)^2(x-3)
    I need to state whether the function is odd or even and i said odd since there is a degree of 3, and the x and y intercepts i solved for and ended up with y=-2 and x=3,1/2. now i need to find the first and second derivative, and i was wondering if i should use the chain rule and product rule ?
    It is even if and only if g(x)=g(-x) and odd if and only if g(x)=-g(-x).

    So does g(1)=g(-1)?

    or does g(1)=-g(-1)?

    CB
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  4. #4
    Junior Member surffan's Avatar
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    i'll solve it like that then, i didnt think of that, thats what you get for working on these problems at 2am. do my derivatives look right though?
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by surffan View Post
    i'll solve it like that then, i didnt think of that, thats what you get for working on these problems at 2am. do my derivatives look right though?
    No your derivative is wrong.

    CB
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  6. #6
    Junior Member surffan's Avatar
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    how should i approach this function in order to get the derivatives? Since its factored im not really sure what i'm suppose to do.
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by surffan View Post
    how should i approach this function in order to get the derivatives? Since its factored im not really sure what i'm suppose to do.
    Product rule followed by chain rule:

    \frac{d}{dx}\left[(1-2x)^2(x-3)\right]=\left[\frac{d}{dx}(1-2x)^2 \right] (x-3) + (1-2x)^2\left[ \frac{d}{dx}(x-3) \right]

    CB
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