Question
Find the intervals in which the function$ f(x) = 3x^4- 4x^3 - 12x^2 + 5$ is
- strictly increasing.
- strictly decreasing.
✓
Answer
$f'(x) = 12x^3 – 12x^2 – 24x = 12x (x + 1) (x – 2)$
$f'(x) > 0, " \forall\text{x}\in( -1 ,0)\text{U}(2,\infty)$
$f'(x) < 0, " \forall\text{x}\in( - \infty, -1 )\text{U}(0,2)$
$\therefore\text{f}(\text{(x})$ is strictlyincreasing in $( - 1, 0 )\text{U}(0,2)$
and strictlydecreasing in $( - \infty, - 1)\text{U}(0,2).$
$f'(x) > 0, " \forall\text{x}\in( -1 ,0)\text{U}(2,\infty)$
$f'(x) < 0, " \forall\text{x}\in( - \infty, -1 )\text{U}(0,2)$
$\therefore\text{f}(\text{(x})$ is strictlyincreasing in $( - 1, 0 )\text{U}(0,2)$
and strictlydecreasing in $( - \infty, - 1)\text{U}(0,2).$
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