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

Question

Find the intervals in which the following functions are increasing or decreasing. $f(x) = 2x^2 - 24x + 7$

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Answer

We have
$f(x) = 2x^2 - 24x + 7$
$f'(x) = 6x^{2 }- 24$
Critical points
$f'(x) = 0$
$\Rightarrow 6x^{2 }- 24 = 0$
$\Rightarrow 6x^2= 24$
$\Rightarrow x^2 = 4$
$\Rightarrow x = 2, -2$
Clearly, $f'(x) >$ 0 if $x > -1$ and $x < -2$
$f'(x) < 0$ if $-2\leq\text{x}\leq2$
Thus, $f(x)$ increasing in $(-\infty,-2)\cup(2,\infty),$ decreasing in $(-2, 2).$

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