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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 $2{x^2} + x - 1$ is
  • A
    $ - {1 \over 4}$
  • B
    ${3 \over 2}$
  • ✓
    ${{ - 9} \over 8}$
  • D
    ${9 \over 4}$
✓

Answer

Correct option: C.
${{ - 9} \over 8}$
c
(c) $f(x) = 2{x^2} + x - 1$

==> $f'(x) = 4x + 1 \Rightarrow f'(x) = 0 \Rightarrow x = - \frac{1}{4}$

$f''\,(x) = 4 = + ve$

$\therefore {[f( - 1/4)]_{\min }} = \frac{2}{{16}} - \frac{1}{4} - 1 = \frac{{ - 9}}{8}$.

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