# 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