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

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

correct answer:

b.(19,-2)