Differentiability

Is the function is the following graph differentiable at x = 0?

• Yes

• No

Is the above function differentiable for all values of x?

• Yes

• No

In which quadrant of the graph above will there be a value of x that is non-differentiable?

• 1

• 2

• 3

• 4

Tags

CCSS.8.F.A.3

Is the above function differentiable at x = 0? Why?

• No, cusp

• Yes

• No, discontinuity.

• No, corner.

Is the above function differentiable at

x = 0? Why?

• Yes

• No, there is a vertical tangent.

• No, cusp

• No, the function is not continuous

Which of the following would be a valid reason the above function is non-differentiable at x = 0?

• The graph contains a corner.

• The graph contains a cusp.

• The graph contains a discontinuity.

• The graph contains a vertical tangent.

Tags

CCSS.8.F.A.3

• Differentiable for all real numbers.

• Not diff. at (0,0).

• Not diff at (2,3).

•  Not diff at (-2,3).

• True

• False

For what value(s) of x is the function continuous but not differentiable?

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

For what values of x in the domain of the above function does the function to appear differentiable?

• (-2, 3)

• Nowhere

• Everywhere except x=-1