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Application of Derivatives — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsApplication of Derivatives1 Mark
MCQ
If $f(x)=x^3-6 x^2+9 x+3$ be a decreasing function, then $x$ lies in
  • A
    $(-\infty,-1) \cap(3, \infty)$
  • ✓
    $(1,3)$
  • C
    $(3, \infty)$
  • D
    None of these
✓

Answer

Correct option: B.
$(1,3)$
(b) : Given, $f(x)=x^3-6 x^2+9 x+3$
$\therefore f^{\prime}(x)=3 x^2-12 x+9=3\left(x^2-4 x+3\right)$
For decreasing, $f^{\prime}(x)<0$
$\Rightarrow \quad(x-3)(x-1)<0 \therefore x \in(1,3)$

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