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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The value of $x$ for which $\left(x-x^2\right)$ is maximum, is
  • A
    $3 / 4$
  • B
    $1 / 2$
  • C
    $1 / 3$
  • D
    $1 / 4$
✓

Answer

Let $f(x)=x-x^2 \therefore f^{\prime}(x)=1-2 x$
For critical point, $f^{\prime}(x)=0 \Rightarrow 1-2 x=0 \Rightarrow x=1 / 2$
Now, at $x=1 / 2, f^{\prime \prime}(x)=-2<0$
So, $f(x)$ has maximum value at $x=1 / 2$.

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