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