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)

Question

Erica Dillon

Mathematics

2 May, 03:20

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)

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Answers (1)

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Braydon · Answer 1

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