What is the Area of this Rectangle? And X Intercepts?

Question

1) Find the maximum area possible 

2) Find the x intercepts. What do they represent in this situation? 

Answer 1

(1)

Step 1:

Length of the rectangle is .

Breadth of the rectangle is .

Area of the rectangle is .

.

Differentiate on each side with respect to .

Product rule of derivatives: .

.

Step 2:

For maximum or minimum values eqaute the first derivative to zero.

Use second derivative test to determine whether it is maximum or minimum.

Consider

Differentiate on each side with respect to .

.

Therefore rectangle has maximum area at .

Maximum area of the rectangle is square units.

Solution:

Maximum area of the rectangle is  square units.

Answer 2

(2)

Area of the rectangle is .

Find the -intercepts by eqauting .

 and .

-intercepts of the function represents the end points of domain of the area function.