Constructing a box. From a rectangular piece of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by cutting out identical squares of area x^2 from each corner and turning up the sides.

(a) Show that the volume of the box is given by the function V(x)=x(20-2x)(30-2x).

(b) Find all positive values of x such that V(x)0.

Question

Constructing a box. From a rectangular piece of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by cutting out identical squares of area x^2 from each corner and turning up the sides.

(a) Show that the volume of the box is given by the function V(x)=x(20-2x)(30-2x).

(b) Find all positive values of x such that V(x)>0.

anonymous · Answer

height=x
length=20-2(what u cut out)=20-2x
width=30-2(what u cut out)=30-2x
so v(x)=l*w*h=x(20-2x)(30-2x)

b) (0,10)