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) = 10 - 6x - 2x²

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Answer

f(x) = 10 - 6x - 2x²
f'(x) = -6 - 4x
For f(x) to be increasing, we must have
f'(x) > 0
⇒ -6 - 4x > 0
⇒ -4x > 6
$\Rightarrow\text{x}<\frac{-3}{2}$
$\Rightarrow\text{x}\in\Big(-\infty,\frac{-3}{2}\Big)$
So, f(x) is increasing on $\Big(-\infty,\frac{-3}{2}\Big).$
For f(x) to be decreasing, we must have
f'(x) < 0
⇒ -6 - 4x < 0
⇒ -4x < 6
$\Rightarrow\text{x}>\frac{-6}{4}$
$\Rightarrow\text{x}>\frac{-3}{2}$
$\Rightarrow\text{x}\in\Big(\frac{-3}{2},\infty\Big)$
So, f(x) is decreasing on $\Big(\frac{-3}{2},\infty\Big).$

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