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Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives1 Mark
Question
The value of $x$ for which $\left(x-x^2\right)$ is maximum, is
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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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