# What is the equation of the line that is normal to #f(x)= lnx^2-x# at # x= 1 #?

##### 1 Answer

#### Explanation:

A *normal line* is simply a line perpendicular to a tangent line. We are being asked to find the normal line at

**Step 1: Find the Derivative**

Note first that

And that's all for this step.

**Step 2: Evaluate**

Here, we evaluate

But we don't want the slope of the tangent line, we want the slope of the normal line. Luckily, there is a simple relationship between tangent line and normal line slopes: they are opposite reciprocals. That is to say:

Normal line slope=-1/tangent line slope

In our case, that means the normal line slope is

**Step 3: Normal Line Equation**

Normal lines, like tangent lines, are of the form

Now we can solve for

The equation of the normal line is therefore