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

Question

Find the intervals in which the following functions are increasing or decreasing.
$f(x) = 2x^3 - 9x^2 - 12x + 1$

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Answer

$f(x) = 2x^3 - 9x^2 - 12x + 1$
$f'(x) = -6x^2 - 18x - 12$
Critical points
$f'(x) = 0$
$\Rightarrow -6x^2 - 18x - 12 = 0$
$\Rightarrow x^2 + 3x + 2 = 0$
$\Rightarrow (x + 2)(x + 1) = 0$
$\Rightarrow x = -2, -1$
Clearly, $f'(x) > 0$ if $x < -1$ and x > -2
f'(x) < 0 if -2 < x < -1
Thus, f(x) increasing in (-2, -1) decreasing in $(-\infty,-2)\cup(-1,\infty).$

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