# What is the equation of the line normal to #f(x)=4/(2x-1) # at #x=0#?

##### 1 Answer

*A normal line* is a line that is perpendicular to the tangent. In other words, we must first find the equation of the tangent.

#### Explanation:

**Step 1: Determine which point the function and the tangent pass through**

**Step 2: Differentiate the function**

Let

Then,

The derivative of

We can now use the quotient rule, as shown above, to determine the derivative.

**Step 3: Determine the slope of the tangent**

The slope of the tangent is given by evaluating

Then, we can say:

**Step 4: Determine the slope of the normal line**

As mentioned earlier, the normal line is perpendicular, but passes through the same point of tangency that does the tangent. A line perpendicular to another has a slope that is the *negative reciprocal* of the other. The negative reciprocal of

**Step 5: Determine the equation of the normal line using point-slope form**

We now know the slope of the normal line as well as the point of contact. This is enough for us to determine its equation using point-slope form.

**In summary...**

The line normal to

**Practice exercises:**

Determine the equation of the normal lines to the given relations at the indicated point.

a)

b)

c)

d)

Hopefully this helps, and good luck!