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An open box is to be made out of a 6-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.a) Find the volume of the open box as a function of x, where x represents the height of the open box. V(x) = x(6-2x)(18-2x)b) Find the first derivative of the open box, with respect to x.V'(x) = 36x - 48x^2 216 - 12x^2 - 36xc) Find the dimensions of the resulting box that

An open box is to be made out of a 6-inch by 18-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume.a) Find the volume of the open box as a function of x, where x represents the height of the open box. V(x) = x(6-2x)(18-2x)b) Find the first derivative of the open box, with respect to x.V'(x) = 36x - 48x^2 216 - 12x^2 - 36xc) Find the dimensions of the resulting box that

1 viewsDec 3, 2021

SOLVED:Numerical and Graphical Analysis You plan to construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (check your book to see figure) (a) Write a function V that represents the volume of the box. (b) Determine the domain of the function V. (c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x) . Use the table to estimate the

SOLVED:Numerical and Graphical Analysis You plan to construct an open box from a square piece of material, 36 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (check your book to see figure) (a) Write a function V that represents the volume of the box. (b) Determine the domain of the function V. (c) Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V(x) . Use the table to estimate the

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