Differentiability and Discontinuity Concepts

The video tutorial explains the conditions under which a function is not differentiable. It covers three main conditions: discontinuity, sharp corners or cusps, and vertical tangent lines. The tutorial identifies specific x-values where the function is not differentiable due to these conditions, including x = -3, x = 6, x = 0, and x = 3. The video provides a clear understanding of how these conditions affect differentiability and concludes with a summary of the non-differentiable points.

What is one condition under which a function is not differentiable?

• The function has a hole at a point.

• The function is quadratic.

• The function is linear.

• The function is continuous everywhere.

Which of the following is a type of discontinuity that affects differentiability?

• Linear discontinuity

• Removable discontinuity

• Continuous discontinuity

• Quadratic discontinuity

At which x-value does the function have a jump discontinuity?

• x = 3

• x = -3

• x = 0

• x = 6

What feature of a graph indicates a sharp corner or cusp?

• A straight line

• A smooth curve

• A point where the slope is zero

• A point where the slope changes abruptly

At which x-value does the function have a sharp corner or cusp?

• x = 3

• x = 6

• x = 0

• x = -3

Why is a function not differentiable at a point with a sharp corner?

• The slopes from the left and right are the same.

• The slopes from the left and right are different.

• The function is continuous at that point.

• The function is linear at that point.

What is the characteristic of a vertical slope in terms of differentiability?

• It is undefined.

• It is well-defined.

• It is infinite.

• It is zero.

At which x-value does the function have a vertical slope?

• x = -3

• x = 0

• x = 3

• x = 6

Which x-values indicate where the function is not differentiable?

• x = -2, x = 1, x = 4, x = 5

• x = -3, x = 0, x = 3, x = 6

• x = -1, x = 2, x = 5, x = 7

• x = 0, x = 1, x = 2, x = 3

What is the overall differentiability status of the function discussed?

• Not differentiable at x = -3, 0, 3, 6

• Not differentiable at x = 1, 2, 3, 4

• Differentiable only at x = 0

• Differentiable everywhere