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I have a piece of metal 10m long and 0.3m wide. I need to bend it into an open U shaped channel (gutter) by bending the 0.3m width twice. I need to use a quadratic equation to to determine where to make the bends to get the maximum volume.

Thankyou for your help. Peter

If the bottom has width x, the height is (0.3-x)/2.

This makes the cross sectional area into x(0.3-x)/2 = 0.15x - 0.5x^2.

Let this be f(x).

Maximize by finding f'(x), setting it to 0, and solving for x.

Note that here f'(x) = 0.15 - x, so the solution is x = 0.15.

This makes the height into (0.3-0.15)/2 = 0.075.

The cross sectional area is then 0.15 x 0.075 = 0.01125.

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Comment | Thank you Scott. Much appreciated answer and easy to understand. |

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