Optimization

A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges.What will be the dimensions of the box with longest volume?

v=(-2)(3-2x)(x)+(4-2x)(-2)(x)+(4-2x)(3-2x)(1)

  =-6xt4x^2-8x+4x^2+4x^2-14x+12

  =12x^2-28x+12

  =4(3x^2-7x+3)

x=(-(-7)±√((-7) 〖^2〗-4(3)(3)))/(2a2(3))=(7±√13)/6

x=0.57 or x=1.77