There doesn’t need to be an inflection point to switch between concave and convex if there are points where the function is undefined.Sarah66 said:
No, a point of inflection can be either concave or convex depending on the direction of the curve at that point.
You can determine the direction of the curve at a point of inflection by looking at the concavity of the curve on either side of the point. If the curve is concave up on one side and concave down on the other, the point of inflection is concave. If the curve is concave down on both sides or concave up on both sides, the point of inflection is convex.
No, a point of inflection can only be either concave or convex. It cannot be both at the same time.
Knowing the direction of a point of inflection can help in analyzing the behavior of a curve and understanding its properties. It can also be useful in determining the maximum or minimum points of a curve.
Both answers can be correct depending on the direction of the curve at the point of inflection. Therefore, it is important to specify the direction when discussing a point of inflection.