# Can anybody help me with this optimization problem?

##
A rectangle has one vertex at the origin, one of the x-axis, one on the y-axis, and one on the graph of #y=sqrt(4-x)#

What is the largest the rectangle can have, and what are its dimensions?

This is everything I've figured out so far. I'm guessing that

#A=xy#

and

#A=x(sqrt(4-x))#

But I don't know how to continue

Thank you!

A rectangle has one vertex at the origin, one of the x-axis, one on the y-axis, and one on the graph of

What is the largest the rectangle can have, and what are its dimensions?

This is everything I've figured out so far. I'm guessing that

and

But I don't know how to continue

Thank you!

##### 1 Answer

Dimensions of largest rectangle are

#### Explanation:

By largest one means largest area.

As area is given by

it will be maximized when

As

=

and

or

=

=

and

or

Dimensions of largest rectangle are

and its area is

Below is graph of

graph{xsqrt(4-x) [-3.063, 6.937, -1.12, 3.88]}