What does it mean about a point if the tangent line has a slope of 0?
1 Answer
Aug 24, 2016
A line with a slope of 0 is simply a horizontal line
Explanation:
As I said, the tangent is horizontal at that point. It has also meaning in terms of maxima and minima for the function. Since the tangent is horizontal at the point, this point is a good candidate for local minimum or minimum at the point (a critical point) . See for example the following local minimum
graph{x^2+1 [-10, 10, -5, 5]}
where the tangent
However, a
graph{x^3+1 [-10, 10, -5, 5]}
Where the slope is