Function f(x) = 2 x^3 - 9 x^2 + 12x + 29 is monotonically decreas… - Vidyadip

MCQ

Function $f(x) = 2{x^3} - 9{x^2} + 12x + 29$ is monotonically decreasing, when

A
$x < 2$
B
$x > 2$
C
$x >1$
✓
$1< x < 2$

✓

Answer

Correct option: D.

$1< x < 2$

d
(d) Function is monotonically decreasing, when $f'(x) < 0$

==> $6{x^2} - 18x + 12 < 0$ ==> ${x^2} - 3x + 2 < 0$

==> ${x^2} - 2x - x + 2 < 0$ ==> $(x - 2)(x - 1) < 0$,

$\therefore x \in 1 < x < 2$.

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