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

##### 2 Answers

The equation is

#### Explanation:

We start by finding the y-coordinate at the given x-point.

We can start by simplifying the function.

We now use the chain rule to differentiate

Let

The slope of the *tangent* is given by evaluating

The normal line is *perpendicular* to the tangent, that's to say its slope is the negative reciprocal of that of the tangent.

The equation of the normal line can be found using a point

Hopefully this helps!

#### Explanation:

To make f real,

At

Its equation is

graph{(ysqrt(x+2)-1)(2x-y+3)=0x^2 [-10, 10, -5, 5]}