Question

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

• A. $1/2$
• B. $1/4$
• C. $3/4$
• D. $1/3$

Answer 1

The correct option is A $1/2$

Let a function be,

$f\left(x\right)=x-x^2$, we have to find the maximum value of $f\left(x\right)$.

For this differentiating $f\left(x\right)$ we get $f^{\prime }\left(x\right)=1-2x$, equating to $0$ gives: $1-2x=0$

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