Question
Find the intervals in which the function $f(x)=3 x^4-4 x^3-12 x^2+5$ is (a) strictly increasing (b) strictly decreasing.
✓
Answer
$f^{\prime}(x)=12 x^3-12 x^2-24 x$
= 12x(x + 1)(x - 2)
$f^{\prime}(x)>0, \forall x \in(-1,0) \cup(2, \infty)$
$f^{\prime}(x)<0, \forall x \in(-\infty,-1) \cup(0,2)$
$\therefore f(x)$ is strictly increasing in $(-1,0) \cup(2, \infty)$
and strictly decreasing in $(-\infty,-1) \cup(0,2)$
= 12x(x + 1)(x - 2)
$f^{\prime}(x)>0, \forall x \in(-1,0) \cup(2, \infty)$
$f^{\prime}(x)<0, \forall x \in(-\infty,-1) \cup(0,2)$
$\therefore f(x)$ is strictly increasing in $(-1,0) \cup(2, \infty)$
and strictly decreasing in $(-\infty,-1) \cup(0,2)$
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