If f(x) = k x^3 - 9 x^2 + 9x + 3 is monotonically increasing in e… - Vidyadip

MCQ

If $f(x) = k{x^3} - 9{x^2} + 9x + 3$ is monotonically increasing in each interval, then

A
$k < 3$
B
$k \le 3$
✓
$k > 3$
D
None of these

✓

Answer

Correct option: C.

$k > 3$

c
(c) $f'(x) = 3k{x^2} - 18x + 9 = 3\,\,[k{x^2} - 6x + 3] > 0,\,\,\forall x \in R$

$\therefore \Delta = {b^2} - 4ac < 0\,\,\,,k > 0$

$i.e.,\;\;36 - 12k < 0$ or $k > 3$.

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