Question

The number that exceeds its square by the greatest amount is

• A. $-1$
• B. $0$
• C. $\frac{1}{2}$
• D. $\frac{-1}{2}$

Answer 1

The correct option is C

$\frac{1}{2}$

Explanation for the correct answer:

Let $x$ be the number

Let $y$ be the difference between the number and its square.

$y=x-x^2$

For the difference to be maximum, $\frac{dy}{dx}=0$

$\frac{dy}{dx}=1-2x=0$

$\Rightarrow$ $x=\frac{1}{2}$

Hence, the correct option is $\left(C\right)$