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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
The Function $\text{f}(\text{x})=\frac{\lambda+\sin\text{x}+2\cos\text{x}}{\sin\text{x}+\cos\text{x}}$ is increasing, if:
  • A
    $\lambda<1$
  • B
    $\lambda>1$
  • C
    $\lambda<2$
  • ✓
    $\lambda>2$
✓

Answer

Correct option: D.
$\lambda>2$
$\text{f}(\text{x})=\frac{\lambda+\sin\text{x}+2\cos\text{x}}{\sin\text{x}+\cos\text{x}}$
$\Rightarrow\text{f}(\text{x})=(\lambda-2)\sin^2\text{x}+(\lambda-2)\cos^2\text{x}>0$
Using identity
$\Rightarrow\lambda-2>0$
$\Rightarrow\lambda>2$

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