This is where the second derivative comes into play. The tangent line at 0 is the x -axis regardless of the value of a .
Some authors use concave for concave down and convex for concave up instead.
Usually graphs have regions which are concave up and others which are concave down. Thus there are often points at which the graph changes from being concave up to concave down, or vice versa. These points are called inflection points . I iff on I . It is clear from this result that if c is an inflection point then we must have Example.