You are constructing a cardboard box with the dimensions 4 m by 6 m. You then cut equal-size squares ( x by x squares) from each

Question

2 years ago

15

You are constructing a cardboard box with the dimensions 4 m by 6 m. You then cut equal-size squares ( x by x squares) from each

corner so that you may fold the edges to get a box. How long should x be to get a box with the maximum volume?? Round your answer to three decimal places. (enter numbers only)

Mathematics

1 answer:

Vlad1618 [11] · Answer 1 · 2022-08-19T16:47:26+03:00

Vlad1618 [11]2 years ago

7 0

Answer:

0.785 m

Step-by-step explanation:

(4-2x)(6-2x)x = Volume

Volume = 4x³ - 20x² + 24x

Max volume: dV/dx = 0

dV/dx = 12x² - 40x + 24 = 0

3x² - 8x + 6 = 0

x = 2.54858377, 0.784749563

Max when d²V/dx² < 0

d²V/dx² = 6x - 8

At x = 0.784749563

6x - 8 = -3.29 < 0