Question

Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =

• A. 44563
• B. 44565
• C. 44624
• D. 44564

Answer 1

Answer: (A)

44563

Answer 2

$y = x - x^2$, where y is the greatest difference.
Differentiating w.r.t. x, we get
$\Rightarrow \frac{dy}{dx} = 1- 2x \:\:\: \therefore \: \frac{dy}{dx} =0 \Rightarrow x = \frac{1}{2}$
$\Rightarrow \frac{d^{2}y}{dx^{2}}]_{x= \frac{1}{2}} =- 2 <0$
Difference is greatest at $x = \frac{1}{2}$