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#### Petrus

##### Well-known member

- Feb 21, 2013

- 739

My progress:

I rewrite it as \(\displaystyle 5\ln(x)-5x^2-4x≤a\) and then derivate andfind the ciritical point

\(\displaystyle f'(x)=\frac{5}{x}-10x-4\)

\(\displaystyle x_1=\frac{1}{10}(-2-3\sqrt{6})\) (Notice that it says \(\displaystyle x>0\) and this is negative root so we shall ignore it.

\(\displaystyle x_2=\frac{1}{10}(3\sqrt{6}-2)\) (this root work fine!)

then I shall put that x value in \(\displaystyle 5\ln(x)-5x^2-4x\) and I get the answer

http://www.wolframalpha.com/input/?i=5*ln%281%2F10%283sqrt%286%29-2%29%29-5%281%2F10%283sqrt%286%29-2%29%29^2-4%281%2F10%283sqrt%286%29-2%29%29

Is this correct thinking or I am doing wrong?