## Condition of the problem

To derive the equation of the normal to the given curve at the point with abscissa $x_{0}$.

$y=\frac{4 x-x^{2}}{4}, x_{0}=2$
## Solution

Let's find $y^{\prime}:$

$$
y^{\prime}=\left(\frac{4 x-x^{2}}{4}\right)^{\prime}=\frac{4-2 x}{4}=\frac{2-x}{2}
$$

Then:

$y_{0}^{\prime}=y^{\prime}\left(x_{0}\right)=\frac{2-x_{0}}{2}=\frac{2-2}{2}=0$

Since $y^{\prime}\left(x_{0}\right)=0$, the equation of the normal line is:

$x=x_{0}$

$x=2$

Thus, the equation of the normal line is:

$x=2$

## Problem Kuznetsov Differentiation 3-1