What is the equation of the line normal to #f(x)=(2x^2 + 1) / x# at #x=-1#?
1 Answer
The normal line is given by
Explanation:
Rewrite
Then, using the power rule,
When
Also, when
If we have the slope to the tangent
Therefore, we know that the normal line is of the form
We know that the normal line passes through
Substitute
You can verify this on a graph:
graph{(y-(2x^2+1)/x)(y+x+4)((y+3)^2+(x+1)^2-0.01)=0 [-10, 10, -5, 5]}