Question

an open box is to be made from a two-foot by three-foot rectangular piece of metal by cutting equal squares from the corners and turning up the sides. find the volume of the largest box that can be made in this manner. round your final answer to the nearest hundredth.

Answer 1

The volume for the largest box will be 1.056 foot³. This can find out by application of differentiation.

What is AOD?

AOD is nothing but application of differentiation. It implies scopes where we can use differentiation to make our calculations easy.

Here, given

Length and breadth = 2,3 foot

Let us consider length of side of square = x

So, after cutting squares left sides of rectangular sheet = 2-2x , 3-2x

So, volume = (2-2x)*(3-2x)*x

                v = 4x³ - 10x² + 6x

To find largest volume , $\frac{dv}{dx}$ = 0

                 $\frac{dv}{dx}$ = 12x² - 20x + 6

                12x² - 20x + 6 = 0

                x = 0.4 , 1.3

But, for 1.3 volume will be negative i.e. not possible.

So, volume = 2.2*1.2*0.4

                   = 1.056 foot³

Learn more about differentiation from given link:

brainly.com/question/954654

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