MCQ
The minimum value of the expression $7 - 20x + 11{x^2}$ is
- A${{177} \over {11}}$
- B$ - {{177} \over {11}}$
- ✓$ - {{23} \over {11}}$
- D${{23} \over {11}}$
$f'(x) = - 20 + 22x$
Put $f'(x) = 0$ $i.e.,$ $ - 20 + 22x = 0$
==> $x = 10/11$ and $f''(x) = 22 > 0$
Hence at $x = 10/11,\;\;\;f(x)$ will have minimum value,
$\therefore f\,\left( {\frac{{10}}{{11}}} \right) = 7 - \frac{{200}}{{11}} + \frac{{100 \times 11}}{{121}}$$ = 7 - \frac{{200}}{{11}} + \frac{{100}}{{11}}$
$ = - \frac{{23}}{{11}}$.
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$f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }$