# What is the equation of the line that is normal to #f(x)= x^3-4x# at # x=0 #?

##### 1 Answer

#### Explanation:

A normal line is a straight line perpendicular to a tangent line. Since perpendicular lines have opposite reciprocal slopes, the way we find a normal line is to find the slope of a tangent line and then do the opposite reciprocal stuff.

But what is the slope of the tangent line at

That means the slope of the tangent line of

The slope of the normal line is perpendicular to this, so we take the opposite reciprocal of

Opposite reciprocal of

However, we're being asked for the *equation* of the normal line, not just the slope. As a result, we still have some more work to do. Recall that straight lines (the normal line is straight) take the form

Note that if we find a point

Our point is

Making substitutions in

The