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

##### 1 Answer

The equation of the normal line is

#### Explanation:

We have the function,

At

So, the point is at

First, we find the slope of the tangent line at

So at

Now, the normal line is perpendicular to the tangent line, and we know that the slope of the normal line is the negative reciprocal of the tangent line, as

And so, the slope becomes,

The point-slope form states that,

And so,

Here is a graph of the line: