# Do you count undefined points in the concavity?

## Question:

Do you count undefined points in the concavity?

## Functions:

For a function {eq}y=f(x) {/eq} defined in the Cartesian plane, the first derivative test tells us about the increasing/decreasing nature of the function whereas the second derivative test for a function tells us about the concavity, as well as the inflection points of a function, i.e. the points at which the second derivative is zero or undefined.

As we know that the concavity is calculated by the second derivative test. For a function, whose second derivative at a point is positive, we can say the concavity of that function to be upward at that point, whereas for a function whose second derivative is negative at a point, we can say the concavity to be downward at that point.

Now, the inflection point is a point at which the second derivative is undefined or zero.

Hence, concavity does not counts the undefined points, rather it counts the curvature of the function. 