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

##### 1 Answer

May 20, 2016

See below.

#### Explanation:

I'll first explain my reasoning for what I'm about to do:

Find the derivative of the function

Find the gradient of the tangent at

Find the gradient of the normal line at

Find the y-coordinate at

Find the equation of the normal line with the above information

Firstly

Therefore the gradient at

Therefore the gradient of the normal line at

The y-coordinate of the function at

Finally,

In general a straight line is given by:

By substituting what we know:

Finally: