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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
Let $3f(x) - 2f(1/x) = x,$ then $f'(2)$ is equal to
  • A
    $2/7$
  • ✓
    $1/2$
  • C
    $2$
  • D
    $7/2$
✓

Answer

Correct option: B.
$1/2$
b
(b) $3f(x) - 2f(1/x) = x$ .....$(i)$

Let $1/x = y$, then $3f(1/y) - 2f(y) = 1/y$

==> $ - 2f(y) + 3f(1/y) = 1/y$

==> $ - 2f(x) + 3f(1/x) = 1/x$ .....$(ii)$

$From \,\, 3 × (i) + 2 × (ii),$

$9f(x) - 6f(1/x) - 4f(x) + 6f(1/x) = 3x + 2/x$

$5f(x) = 3x + \frac{2}{x}$ 

==> $f(x) = \frac{1}{5}\left[ {3x + \frac{2}{x}} \right]$

==> $f'(x) = \frac{1}{5}\left[ {3 - \frac{2}{{{x^2}}}} \right]$

==> $f'(2) = \frac{1}{5}\left[ {3 - \frac{2}{4}} \right] = \frac{1}{2}$.

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