Question

maximum area of rectangle when area A is given by A=(x-1)(24/x)​

Answer 1

Step-by-step explanation:

Let the base of the rectangle be denoted by the points on the x axis

(x,0) and (−x,0).

Then the rest of the two vertices will be (−x,3−x),(x,3−x).

Hence length of the base of the rectangle=2x.

Height of the rectangle=3−x.

Hence area

A=2x(3−x)

=6x−2x

2

dx

dA

=6−4x

=0

x=

2

3

.

Then

Area

max

=2x(3−x)

=2.

2

3

(3−

2

3

)

=

2

9

sq units.