[填空题]
A company that manufactures and serh5 z 6j*db7holz1m kfh 63wic+0qdal5o/gt4 h -iw uo9ls cardboard boxes has a box with an open-top1ho04gfk 3dw iil tam6/w zoqu9-c5h+ design. This box is constructed from a rectangular cardboard sheet with a length of 2 meters and a width of 1.2 meters, as illustrated in the diagram below. The box is formed by cutting squares of equal side length ( x meters) from each corner and folding up the sides.
1. Show that the volume of the box can be described by the function $V(x)= 4 x^{3}-6.4 x^{2}+2.4 x $.
2. 1. Find $V^{\prime}(x)$= ax$^2$-bx+c;a= ,b= .c= .
2. Hence or otherwise, find the value for x that maximises the volume of the box;
x= m
3. Hence, find the maximum volume of the box.
3. Sketch the graph of V(x) on the axes below for the domain 0 4. 1. Write down an integral representing the area between the graph of V(x) and the x -axis;
2. Hence, find this area between the graph of V(x) and the x -axis.
Let A(x) be a function representing the outside surface area of the box.
5. Determine the function A(x) .
A(x)=-ax$^2$+b;a= ,b= .
6. Given that the volume of the box is maximised, find the outside surface area of the box.
