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STD 12 - 6. Application of derivatives — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 6. Application of derivatives1 Mark
MCQ
The function $f(x) = ax + {b \over x};a,\,b,x > 0$ takes on the least value at  $x$  equal to
  • A
    $b$
  • B
    $\sqrt a $
  • C
    $\sqrt b $
  • ✓
    $\sqrt {b/a} $
✓

Answer

Correct option: D.
$\sqrt {b/a} $
d
(d) $f(x) = ax + \frac{b}{x}$ ==> $f'(x) = a - \frac{b}{{{x^2}}}$

==> $f'(x) = 0 \Rightarrow x = \sqrt {\frac{b}{a}} $

Now $f''(x) = \frac{{2b}}{{{x^3}}}$ ==> At $x = \sqrt {\frac{b}{a}} ,$ $f''(x) = + ve$

$\therefore$ $f(x)$ has the least value at $x = \sqrt {\frac{b}{a}} $.

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