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**user_5** A cuboid tank is open at the top and the internal dimensions of its base are x m and *2x* m.

The height is *h* m.

The volume of the tank is *V* cubic metres and the volume is fixed. Let *S mē *denote the internal surface area of the tank.

S in terms of x and h

$\displaystyle S=2(2xh)+2x(x)+2(hx)$

$\displaystyle S=2x^2+6xh$

S in terms of V and x

$\displaystyle V=2x * x * h $

$\displaystyle V=2x^2h$

$\displaystyle h=\frac{V}{2x^2}$

$\displaystyle S=2x^2+6xh$

Sub $\displaystyle h=\frac{V}{2x^2}$

$\displaystyle S=2x^2+6x\left(\frac{V}{2x^2}\right)$

$\displaystyle S=2x^2+\frac{3V}{x}$

The maximal domain of *S* in terms of *V* and *x* is $\displaystyle (0,\infty)$

If $\displaystyle 2<x<15$ find the maximum value of *S* if $\displaystyle V = 1000m^3$

I'm stuck here, can anyone please help?