6 The horizontal base of a solid prism is an equilateral triangle of side \(x \mathrm {~cm}\). The sides of the prism are vertical. The height of the prism is \(h \mathrm {~cm}\) and the volume of the prism is \(2000 \mathrm {~cm} ^ { 3 }\).
- Express \(h\) in terms of \(x\) and show that the total surface area of the prism, \(A \mathrm {~cm} ^ { 2 }\), is given by
$$A = \frac { \sqrt { } 3 } { 2 } x ^ { 2 } + \frac { 24000 } { \sqrt { } 3 } x ^ { - 1 }$$
- Given that \(x\) can vary, find the value of \(x\) for which \(A\) has a stationary value.
- Determine, showing all necessary working, the nature of this stationary value.