# What is the equation of the normal line of #f(x)=4x^4+8x^3-2x^2+x-3# at #x=-1#?

##### 1 Answer

#### Explanation:

Let's start by writing down the equation of the normal line we are trying to find:

The slope of a normal to a line with slope,

If we can get slope of the tangent line to our function, we can use this expression to find the slope of the normal line. The slope of the tangent is just the first derivative of the function evaluated at the point of interest. The derivative is:

the slope is then

Therefore the slope of the normal line at is

Finally, to get the equation of the normal line we need to find the y-intercept,

Plugging this into the equation for the normal line we get:

which gives

Finally, the equation of the normal line is

graph{((y+x/13+131/13) (y-(4x^4+8x^3-2x^2+x-3)))=0 [-20, 20, -19, 1]}