# What is the equation of the normal line of #f(x)=sqrt(x^3-x+4)# at #x=2#?

##### 1 Answer

#### Explanation:

We begin by finding the derivative of the function

The slope of the tangent line at

The slope of the normal line is therefore the negative reciprocal of this slope:

To get the equation of the line, we need to find a point to substitute into the equation to get the y-intercept - we need the value of the function at

Substituting this into the equation of the line we obtain

Solving for

Therefore the equation of the normal line to our function at