What is the equation of the line normal to #f(x)=x ^3-x^2 # at #x=-2#?
1 Answer
The equation of the normal line is
Explanation:
We have the function,
At
So, the point is at
First, we find the slope of the tangent line at
So at
Now, the normal line is perpendicular to the tangent line, and we know that the slope of the normal line is the negative reciprocal of the tangent line, as
And so, the slope becomes,
The point-slope form states that,
And so,
Here is a graph of the line: