What is the equation of the normal line of #f(x)=-2x^3-8x^2-2x# at #x=-1#?
To compute the equation of the normal line, you need:
- the slope of the normal line
- one point that is on the normal line
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
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
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!