Given a graph of f' learn to find the points of inflection

The video tutorial discusses concavity and how to identify points of inflection on a graph. It explains that non-differentiable points, such as corners or cusps, are potential points of inflection. The tutorial also covers how to analyze slopes to determine actual points of inflection, focusing on changes in concavity and slope direction.

What is a key characteristic of points where the second derivative is undefined?

• They are always points of inflection.

• They indicate a change in concavity.

• They are corners or cusps on the graph.

• They have a horizontal tangent.

Which of the following x-values is mentioned as a possible point of inflection due to non-differentiability?

• X = -2

• X = -4

• X = 0

• X = 6

Why is X = -1 considered a possible point of inflection?

• It is a point where the slope is negative.

• It is a point where the graph is non-differentiable.

• It is a point where the derivative is zero, creating a horizontal tangent.

• It is a point where the slope is positive.

What indicates a true point of inflection on a graph?

• A constant slope.

• A change in slope from positive to positive.

• A change in slope from negative to negative.

• A change in slope from positive to negative or vice versa.

At which x-value does the slope change from negative to positive, indicating a point of inflection?

• X = -1

• X = 3

• X = -4

• X = 5