What is the equation of the normal line of #f(x)=1/sqrt(x^2-2x+1)# at #x=2 #?
Let's start by simplifying the function.
Now, let's start by finding the corresponding y-coordinate to
Next, let's differentiate the function.
By the quotient rule:
The slope of the tangent (the line that touches the graph at the point
The normal line is perpendicular to the tangent. So, the slope of the normal line is
We now know the normal line's point of contact on the function
Hence, the equation of the normal line is
Hopefully this helps!