Vikolers6

## Answered question

2021-12-17

How to find the intervals of increasing and decreasing using the first derivative given $y=-2{x}^{2}+4x+3$?

### Answer & Explanation

Robert Pina

Beginner2021-12-18Added 42 answers

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.

Cassandra Ramirez

Beginner2021-12-19Added 30 answers

O, god, thank you!

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