[填空题]
A company that manufactures and sells cardb60ac29do t3tw qj 4taioard boxes has a box with an open-toi(s h+ry.:glbp design. This box is constructed from a rectangular cardboard sheet with a length of 2 meters and a widthbi(sg.r ly :+h 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 $V^{\prime}(x)$= a$x^3$ - 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$x^2$ + b ;a= ,b= .
6. Given that the volume of the box is maximised, find the outside surface area of the box.
