MCQ
Function
$f\left( x \right) = \int_1^x {\left\{ {2\left( {t - 1} \right){{\left( {t - 2} \right)}^3} + 3{{\left( {t - 1} \right)}^2}{{\left( {t - 2} \right)}^2}} \right\}} dt$ is maximum when $x$ is equal to
- ✓$1$
- B$2$
- C$3$
- D$4$
$f\left( x \right) = \int_1^x {\left\{ {2\left( {t - 1} \right){{\left( {t - 2} \right)}^3} + 3{{\left( {t - 1} \right)}^2}{{\left( {t - 2} \right)}^2}} \right\}} dt$ is maximum when $x$ is equal to
$\Rightarrow f^{\prime}(x)=2(x-1)(x-2)^{3}=0$ for extrema. $\Rightarrow x=1,2$
Also $f^{\prime}(x)=2(x-2)^{2}+6(x-1)(x-2)^{2}$
Clearly $f^{\prime \prime}(1)<0$ and $f^{\prime \prime}(2)=0$
Hence $x=1$ is the point of maxima.
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