2. a box with an open top is to be constructed from a square piece of cardboard, 3 ft wide, by cutting out a square from each of the four corners and bending up the sides. find the largest volume of the box

Step-by-step explanation:

We are given that

Side of square shaped piece= 3ft

Let  square of side x cut from each corner of square piece cardboard.

Length of box=

Breadth of box=

Height of box= x

We have to find the largest volume of box.

Volume of box is given by

Differentiate w.r.t x

Substitute

Again differentiate w.r.t x

Substitute

Substitute

Therefore, at

Hence, the volume is maximum at

Substitute the value then we get

expression #3 is not equivalent. the others are.

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step-by-step explanation: