A rectangular page is to have a printed area of 62 square inches. If the border is to be 1 inch wide on top and bottom and only 1/2 inch wide on each side find the dimensions of the page that will use the least amount of paper
Can someone explain how to do this?
I started with:
$$A = (x + 2)(y + 1) $$
Then I isolate y and come up with my new equation:
$$A = (x+2)\left(\frac{62}{x + 2}{-1}\right)$$
Then I think my next step is to create my derivative, but wouldn't it come out to -1?
Anyways, I would appreciate if someone could give me a nudge in the right direction.
EDIT
How does this look for a derivative?
$$A = \left(\frac{x^2-124}{x^2}\right)$$
Then to solve:
$$ {x} = 11.1 $$
$$ y = 98 / 11.1 $$
Does that seem about right?
If not, the only thing I would have left is setting it to 0 and solving.
Best Answer
Hint: How did you get the term $\left(\frac {98}{x+2}-1\right)$? You should have $62=xy$ to give the desired printable area, so $A=(x+2)(\frac{62}x+1)$. Then, you are right, you should take $\frac {dA}{dx}$ and set it to $0$ to find $x$.