Maximum Of Function

I Am A Math Wizard. · New Member Offline Joined: 17 Oct 2009 Posts: 2

Find the maximum of $f(x)=\frac{25}{4}\sqrt{\dfrac{(x-4)^2x^2}{25x^2-72x+144}}$ over the domain $x \in [0,4]$ .

**Posted:** Fri Nov 06, 2009 7:44 pm

fedja

The coefficient in front and the square root are irrelevant, the denominator is just $9(x-4)^2+16x^2$ , so the task reduces to the minimization of $\frac 9{x^2}+\frac{16}{(4-x)^2}$ . This can be easily done by taking the derivative and finding its (unique and rather ugly) root on $(0,4)$ .

**Posted:** Fri Nov 06, 2009 9:38 pm

Dr Sonnhard Graubner

hello, i have got
$x_{max}=\frac{16}{25}\cdot6^{2/3}-\frac{24}{25}\cdot6^{1/3}+\frac{36}{25}$
$y_{max}=\frac{1}{5}\sqrt{\frac{-41396\cdot 6^{2/3}+270294\cdot6^{1/3}-329616}{8\cdot6^{1/3}-12+3\cdot6^{2/3}}}$
Sonnhard.

**Posted:** Sat Nov 07, 2009 12:40 am