Calculus work problem help?

CALCULUS PROBLEM HELP ASAP W/WORK PLEASE?

• 1. A piece of cardboard measures 22x35inches. Two equal squares are measured from the corners of a 22-inch side. Two equal rectangles are removed from the other corners so that the two tabs can be folded to form a rectangular box with a lid. A.) Write a formula v(x) for the volume of the box B.) Find the domain of V for the problem C.) Find the max volume and the volume of x that gives it PLEASE SHOW ALL WORK IF POSSIBLE, THANKS

• Answer:

  the length of the box is 35 - 2x the width of the box is 22 - 2x the heighth of the box is x so the Volume of the box = lwh so V(x) = (35 - 2x)(22 - 2x)x so V(x) = (770 -114x + 4x²)x so V(x) = 4x³ -114x² +770x so V'(x) a.k.a. dV/dx = 12x² -228x + 770 the critical points will be where V'(x)=0 so 12x² -228x + 770=0 so 6x² -114x + 385=0 so using the quadratic formula we get x = 19 ± sqrt(10686)/6 the natural constraints on the domain are 0<x<11 since the biggest square you can cut is 11x11 (22inch side) so the max volume is V(19 - sqrt(10686)/6) and the x that gives it is 19 - sqrt(10686)/6 I'll let you compute V(19 - sqrt(10686)/6)