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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
For the every value of $ x$ the function $f(x) = {1 \over {{5^x}}}$ is
  • ✓
    Decreasing
  • B
    Increasing
  • C
    Neither increasing nor decreasing
  • D
    Increasing for  $x > 0 $ and decreasing for  $x < 0$
✓

Answer

Correct option: A.
Decreasing
a
(a) $f(x) = {5^{ - x}}$

==>$f'(x) = - {5^{ - x}}{\log _e}5 = - \frac{{{{\log }_e}5}}{{{5^x}}}$

==> $f'(x) < 0$ for all $x$

$i.e.,$ $f(x)$ is decreasing for all $x.$

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