 # How to find the intervals of increasing and decreasing using Vikolers6 2021-12-17 Answered
How to find the intervals of increasing and decreasing using the first derivative given $y=-2{x}^{2}+4x+3$?
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Use the power rule:
$\frac{d}{dx}=-2\left(2\right){x}^{2-1}+4\left(1\right){x}^{1-1}+0$
And remember that ${x}^{0}=1$ and a derivative of a constant is zero
${f}^{\prime }\left(x\right)=-4x+4$
Now, factor
$-4\left(x-1\right)=0$
$x-1=0$
$x=1$
Now you pick numbers in between the interval and test them in the derivative. If the number is positive, the function is increasing and if it's negative the function is decreasing.
For example, pick 0 a number from the left
${f}^{\prime }\left(0\right)=4$
This means that from $\left(-1,\mathrm{\infty }\right)$ the function is decreasing
And from $\left(\mathrm{\infty },1\right)$ the function is increasing.

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