Q108 / 180 · COMEDK 2018 · Mathematics

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

  • Correct answer
    A
    $1 / 2$
  • B
    $1 / 4$
  • C
    $3 / 4$
  • D
    $1 / 3$

Solution

Let the required numbers be $x$. Then, $f(x)=x-x^{2}$ $\Rightarrow \quad f^{\prime}(x)=1-2 x$ For a local maxima or local minima, we must have $$ \begin{aligned} &\quad f^{\prime}(x)=0 \\ &\Rightarrow \quad 1-2 x=0 \\ &\Rightarrow \quad 2 x=1 \Rightarrow x=\frac{1}{2} \end{aligned} $$ Now, $\quad f^{\prime \prime}(x)=-2 < 0$ So, $x=\frac{1}{2}$ is point of local maxima. Hence, required numbers is $\frac{1}{2}$.

Hence, the correct answer is option: 'A'.

Relevant Questions