The function y = 2 x^3 - 9 x^2 + 12x - 6 is monotonic decreasing,… - Vidyadip

MCQ

The function $y = 2{x^3} - 9{x^2} + 12x - 6$ is monotonic decreasing, when

✓
$1 < x < 2$
B
$x > 2$
C
$x < 1$
D
None of these

✓

Answer

Correct option: A.

$1 < x < 2$

a
(a) Here $f(x) = y = 2{x^3} - 9{x^2} + 12x - 6$

$ \Rightarrow $$f'(x) = 6{x^2} - 18x + 12$

Since$f(x)$ is increasing or decreasing in $(a,b)$ according as $f'(x) > 0$ or $ < 0$ for every $x \in (a,b)$.

Hence $f'(x) = 6(x - 2)(x - 1)$ which is obviously decreasing if $x \in (1,2)\,\,\,i.e.,\,1 < x < 2$.

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