What is the extreme (180ln(x)-300)/(x^2) ?

The extreme (180ln(x)-300)/(x^2) is Maximum(e^{13/6},(90)/(e^{13/3)})

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extreme (180ln(x)-300)/(x^2)

extreme

Maximum (e^{\frac{13}{6}}, \frac{90}{e ^{\frac{13}{3}}})

Solution steps

f^{'} (x) = \frac{60 ( - 6 ln ( x ) + 13 )}{x ^{3}}

Find intervals:

Increasing

: 0 < x < e^{\frac{13}{6}},

Decreasing

: e^{\frac{13}{6}} < x < \infty

Plug

x = e^{\frac{13}{6}}

into

\frac{180 ln ( x ) - 300}{x ^{2}} : \frac{90}{e ^{\frac{13}{3}}}

Maximum (e^{\frac{13}{6}}, \frac{90}{e ^{\frac{13}{3}}})

What is the extreme (180ln(x)-300)/(x^2) ?
The extreme (180ln(x)-300)/(x^2) is Maximum(e^{13/6},(90)/(e^{13/3)})