1. ## word problem (rectangular)

a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.

how do i do this question?

would area be a = (2x)(1/(1+x^2)) ?

2. Originally Posted by haebinpark
a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.

how do i do this question?
first, and most important, make a sketch.

then write the area as a function of x ...

$\displaystyle A = xy = \frac{x}{1+x^2}$

now find $\displaystyle \frac{dA}{dx}$ and maximize like you were taught.

3. do i find derivative of a = 1/(1+x^2)?
not derivative of a = (2x)(1/(1+x^2))?

4. Originally Posted by haebinpark
do i find derivative of a = 1/(1+x^2)?
not derivative of a = (2x)(1/(1+x^2))?
once again with more clarity ...

the area of the rectangle in quad I is $\displaystyle A = x \cdot \frac{1}{1+x^2} = \frac{x}{1+x^2}$