Applications and Examples

The rectangle shown here has one side on the positive y-axis, one side on the positive x-axis, and its upper right-hand vertex on the curve What dimensions give the rectangle its largest area, and what is that area?

Step 1 of 3</p>

In this problem, we have to find the dimension of largest area and also find the area.

Step 2 of 3</p>

The curve is given by

By seeing the graph, we can say that the curve is on the positive side of x-axis and y-axis, then the length of rectangle will be and the width of the rectangle will be

So,

The area of the rectangle will be

Differentiate the area of the rectangle with respect to , we get