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6. Application of derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
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
    ${{23} \over {11}}$
✓

Answer

Correct option: C.
$ - {{23} \over {11}}$
c
(c) Given $f(x) = 7 - 20x + 11{x^2}$

$f'(x) = - 20 + 22x$

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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