If f(x) = x^3 - 6 x^2 + 9x + 3 be a decreasing function, then x l… - Vidyadip

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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