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Math Help - Inequalities

  1. #1
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    Inequalities

    What is the smallest value of a for which the inequality is observed for x> 0?
    what i thought is that i put x = 1 and solve it but did not work well
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Inequalities

    You can rearrange to 2 \ln x - 3x^2 - 6x \le a, then find the max value for the left hand side in the interval x>0. That max value is the value for a.
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    Re: Inequalities

    Quote Originally Posted by ebaines View Post
    You can rearrange to 2 \ln x - 3x^2 - 6x \le a, then find the max value for the left hand side in the interval x>0. That max value is the value for a.
    hmmm i still dont get any progress :S
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    MHF Contributor ebaines's Avatar
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    Re: Inequalities

    Quote Originally Posted by Petrus View Post
    hmmm i still dont get any progress :S
    Do you know how to find the max value of a function? Hint - start by finding where the derivative = 0....
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    Re: Inequalities

    Quote Originally Posted by ebaines View Post
    Do you know how to find the max value of a function? Hint - start by finding where the derivative = 0....
    ok i got these
    x=1/6(sqrt(21)-3)
    x=1/6(-3-sqrt(21))
    is this correct? ajnd what shall i do next
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  6. #6
    MHF Contributor ebaines's Avatar
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    Re: Inequalities

    Quote Originally Posted by Petrus View Post
    is this correct?
    Yes, those are the values of x where the derivative is 0. But remember you only need worry about x>0.

    Quote Originally Posted by Petrus View Post
    what shall i do next
    Next step - what is the value of  2 lnx - 3x^2 -6x at this value of x? That's what 'a' is equal to.
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