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APPLICATION OF DERIVATIVES — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAPPLICATION OF DERIVATIVES1 Mark
MCQ
Function $\text{f}(\text{x})=\log_\text{a}\text{x}$ is increasing on R, if:
  • A
    0 < a < 1
  • ✓
    a > 1
  • C
    a < 1
  • D
    a > 0
✓

Answer

Correct option: B.
a > 1
$\text{f}(\text{x})=\log_\text{a}\text{x}=\frac{\log\text{x}}{\log\text{a}}$
$\text{f}'(\text{x})=\frac{1}{\text{x}\log\text{a}}$

Given: f(x) is increasing on R.

$\Rightarrow\text{f}'(\text{x})>0,\forall\ \text{x}\in\text{R}$

$\Rightarrow\frac{1}{\text{x}\log\text{a}}>0,\forall\ \text{x}\in\text{R}$

$\Rightarrow\text{a}>1$

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The correct option is:

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