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    These questions are the bane of my life...

    g(x) = x^3 at c=2

    So far I've got...

     |g(x)-g(3)| = |x-2||x^2 +2x+4|

    Then restricting x by requiring |x-2|<1 so,

    |x-2| < 1 \Rightarrow -1 < x-2 < 1 \Rightarrow 1 < x < 3 \Rightarrow 1 < x^2 < 9

    This is where I get stuck... I'm not sure how to add on the "+2x" to get to x^2 + 2x + 4? Thanks for any help
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    Firstly, simplify your life by realising that you just want to find an upper bound for x^2+2x+4 (for x in range 1 < x < 3).

    So if you find upper bounds for x^2, 2x and 4, you can just add them to get an upper bound for x^2+2x+4.

    You've already done x^2: if 1 < x < 3, we have x^2 < 9.

    Do the same for the other two bits and add.
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    (Original post by DFranklin)
    Firstly, simplify your life by realising that you just want to find an upper bound for x^2+2x+4 (for x in range 1 < x < 3).

    So if you find upper bounds for x^2, 2x and 4, you can just add them to get an upper bound for x^2+2x+4.

    You've already done x^2: if 1 < x < 3, we have x^2 < 9.

    Do the same for the other two bits and add.
    Ahh thankyou so much, didn't even think of doing it separately like that I was just trying to do it in the one go haha. And I will simplify my life by not choosing analysis next year :rolleyes:
 
 
 
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Updated: January 16, 2015
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