The function $f(x)=2 x^3-9 x^2+12 x+29$ is monotonically increasing in the interval

The function $f(x)=2 x^3-9 x^2+12 x+29$ is monotonically increasing in the interval
  1. $(-\infty, 1) \cup(2, \infty)$
  2. $(-\infty, \infty)$
  3. $(2, \infty)$
  4. $(-\infty, 1)$

Solution

$f(x)=2 x^3-9 x^2+12 x+29$ $\Rightarrow f^{\prime}(x)=6 x^2-18 x+12=6(x-1)(x-2)$ sign scheme $\Rightarrow f(x)$ is increasing in the interval $(-\infty, 1) \cup(2, \infty)$

Asked in: MHT CET 2022 (07 Aug Shift 1)

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