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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths6. Application of derivatives1 Mark
MCQ
If $f(x) = {x^3} - 6{x^2} + 9x + 3$ 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
(b) $f(x) = {x^3} - 6{x^2} + 9x + 3$, 

For decreasing $f'(x) < 0$

==> $3{x^2} - 12x + 9 < 0$ 

==> ${x^2} - 4x + 3 < 0$

==> $(x - 3)\,\,(x - 1) < 0$,

$\therefore$ $x \in (1,\,3)$.

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