Question

2. (-/20 Points] DETAILS SCALCET8 4.7.012 MY NOTES Consider the following problem: A box with an open top is to be constructed from a square piece cardboard, 3 ft wide, by cutting out a square from each the four corners and bending up the sides. Find the largest volume that such a box can have. (a) Draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. Find the volumes several such boxes. (b) Draw a diagram illustrating the general situation. Let x denote the length of the side of the square being cut out. Let y denote the length of the base. (c) Write an expression for the volume V in terms of both x and y. V= (d) Use the given information to write an equation that relates the variables x and y. (e) Use part (d) to write the volume as a function of only x. (f) Finish solving the problem by finding the largest volume that such a box can have. V- Need Help? Read It Talk to a Tutor

Answer 1

6 X x x x ** y 3 ff @ Now Volume : N=y. y. & [y-length r=1y²x y-breadth height a from diagram Y = 3 - 2x © Va X (3-2492 Volume va x (3-249² Q个 & Now (. d Ta d (x ) 80 =x (3-200² Differentiating on both sides (ur) unltru] vlax C de 1(3-2832)) + (3-2032. da =.(2(3-209) (-2) + (3-249219 -21 (6-4d) + (3-2012 - 128 + 882 +9+482-122 9-2427120² Set » 9-24 84124²20 > 3(3-844 42²) = 8 4 4²_89 1820 * 4 x ² -21 -bait 320 => 20 (94-1) - 3(2x-1)=0 = (x-1) (94-3) = 0 20-150 com 21-320 * 2x=1 [ Rule out he because Plug x = 1/2 in it would cause sides of box to be ove ve!) = [ (3-2(* -- (2-152-12_f43 07 2013 a ने ar basis