📈🚫 Derivative Doesn't Exist Understanding Kinks on a Graph 📉🤯

In this video, we explore the concept of a kink on a graph and the effect it has on the slope or derivative. We examine what happens when the curve is not smooth and zoom in to study the fine details of the graph.

We draw slope triangles and observe the values of the slope at different points, both to the left and right of the kink. We see how the value of the slope changes very slowly as we zoom in on a smooth curve, but drastically at a kink.

We study two different kinks on the graph and discover different behaviors associated with each. We observe that to the right of one kink, the slope is positive 39, while to the left of the same kink, the slope is negative 35. At the kink itself, there is no defined value for the slope, and it becomes a giant question mark.

By examining kinks on a graph, we gain insights into some of the deeper mysteries of mathematics. We use real mathematical notation for exponents, roots, and inequalities to ensure clarity and precision.

🤔🔍 15 Common Questions Related to Kinks on a Graph

1. What is a kink on a graph?
Answer A kink is a point on a graph where the curve changes direction abruptly.

2. What is the slope of a kink?
Answer The slope of a kink is not defined at the point of the kink itself.

3. Why is the slope not defined at a kink?
Answer At a kink, the curve changes direction abruptly, and the slope cannot be defined as a value.

4. Can a kink be a point of inflection?
Answer No, a kink cannot be a point of inflection because the curve changes direction abruptly, and the concavity changes.

5. How do kinks affect the derivative?
Answer Kinks affect the derivative because the slope is not defined at the point of the kink itself.

6. What is a smooth curve?
Answer A smooth curve is a curve that has no sharp corners, breaks, or kinks.

7. Can a curve have more than one kink?
Answer Yes, a curve can have more than one kink.

8. What is the value of the slope at a kink?
Answer The value of the slope at a kink is not defined.

9. How does zooming in affect the slope at a kink?
Answer Zooming in does not affect the slope at a kink because the slope is not defined at the point of the kink itself.

10. What is the difference between a kink and a cusp?
Answer A kink is a point where the curve changes direction abruptly, while a cusp is a point where the curve has a sharp corner.

11. Can a curve have both a kink and a cusp?
Answer Yes, a curve can have both a kink and a cusp.

12. How does a kink affect the continuity of a function?
Answer A kink does not affect the continuity of a function because the function is still continuous on either side of the kink.

13. Can a kink be smoothed out?
Answer No, a kink cannot be smoothed out because it is an inherent property of the function.

14. What is the difference between a kink and a jump discontinuity?
Answer A kink is a point where the curve changes direction abruptly, while a jump discontinuity is a point where the function has a finite jump in value.

15. Can a kink occur in a straight line?
Answer No,
video intended for those who like to explore math in more depth
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