# What is the equation of the line that is normal to f(x)=2x^3-3x^2+5 at  x=1 ?

##### 1 Answer
Dec 4, 2015

The normal line is the vertical line through the point $\left(1 , 4\right)$. Its equation is $x = 1$

#### Explanation:

At $x = 1$, we have $y = 4$, so the line we want contains the point $\left(1 , 4\right)$

The tangent at that point has slope $f ' \left(1\right)$.
Since $f ' \left(x\right) = 6 {x}^{2} - 6 x$, we get a slope of $0$.

The tangent line is horizontal. The normal line is perpendicular to the tangent line, so the normal line is vertical.