Question

x and y are the sides of two squares such that $y = x - x^2$. The rate of change of the area of the second square with respect to the area of the first square is

• A. $x^2 - x + 1$
• B. $2 x^2 + 2 x - 1$
• C. $2x^2 - 3x + 1 $
• D. $ x^2 + x - 1 $

Answer 1

Answer: (C)

$A_{2} = \left(x-x^{2}\right)^{2} , A_{1} =x^{2} $
$\frac{dA_{2}}{dx} = 2\left(x-x^{2}\right) \left(1-2x\right)$
$ \Rightarrow \frac{dA_{1}}{dx} = 2x \Rightarrow \frac{dA_{2}}{dA_{1}} = 1+2x^{2} - 3x $