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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
The function $\frac{{\sin \,\,(x\, + \,a)}}{{\sin \,\,(x\, + \,b)}}$ has no maxima or minima if
  • A
    $b - a = n \pi , n \in I$
  • B
    $b - a = (2n + 1) \pi , n \in I$
  • C
    $b - a = 2n \pi , n \in I$
  • ✓
    All of these .
✓

Answer

Correct option: D.
All of these .
d
$f (x) =\frac{{\sin \,\,(x\, + \,a)}}{{\sin \,\,(x\, + \,b)}}$

$ f '(x) =\,\frac{{\sin (x + b)\, \times \,\cos (x + a)\, - \,\sin (x + a)\,\cos (x + b)}}{{{{\sin }^2}(x + b)}}\, =\,\frac{{\sin (b - a)}}{{{{\sin }^2}(x + b)}}\,$

If $sin(b - a) = 0$ then $f' (x) = 0$ ==> $f (x)$ will be constant

i.e. $b - a = n\pi$ or $n\pi$

or $b - a = (2n + 1)\pi$ or $b - a = 2n\pi$

then $f (x)$ has no minima

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