Find the intervals in which the following functions are increasin… - Vidyadip

Question

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = 2x^3- 9x^2 + 12x - 5$

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Answer

We have,
$ f(x)=2 x^3-9 x^2+12 x-5 $
$ \therefore f^{\prime}(x)=6 x^2-18 x+12$
Critical points
$ f^{\prime}(x)=0 $
$ \Rightarrow 6\left(x^2-3 x+2\right)=0 $
$ \Rightarrow(x-2)(x-1)=0 $
$ \Rightarrow x=2,1$
Clearly, $f^{\prime}(x)>0$ if $x<1$ and $x>6$
$f^{\prime}(x)<0 \text { if } 1<x<2$
Thus, $f(x)$ increases in $(-\infty, 1) \cup(2, \infty)$, decreases in $(1,2)$.

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