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

##### 1 Answer

#### Explanation:

To compute the equation of the normal line, you need:

- the slope of the normal line
- one point that is on the normal line

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1) Let's start with the **point**.

You already know that the normal line intercepts your function

So, the only thing left to do is computing the

So, your point is

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2) Now, let's take care of the **slope** . To do so, you need to differentiate

This means that the slope of the *tangent line* at

The slope of the *normal line* is

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3) We have the point and the slope. Let's compute the equation of the normal line.

The equation of any line is

We know that

With this knowledge, we can compute

So, the equation of the normal line is

Hope that this helped!