Differentiability and Continuity

Differentiability implies continuity.

• True

• False

Tags

CCSS.HSF-LE.A.1B

Continuity implies differentiability.

• True

• False

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

• corner, cusp, horizontal tangent, discontinuity
• corner, cusp, vertical tangent, continuity
• corner, cusp, vertical tangent, discontinuity
• corner, curve, vertical tangent, continuity

Which of the following would be a valid reason the above function is non-differentiable at x = 2?

• The graph contains a vertical tangent.
  

• The graph contains a cusp.

• The graph contains a discontinuity.

Tags

CCSS.8.F.A.3

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

Which of the following would be a valid reason the above function is non-differentiable at x = 2?

• The graph contains a vertical tangent.
  

• The graph contains a cusp.

• The graph contains a discontinuity.

Tags

CCSS.8.F.A.3

Where is the graph NOT continuous? (SELECT ALL THAT APPLY)

• -5

• -2

• 0

• 1

• 3

Tags

CCSS.HSF-IF.C.7D

Where is the graph continuous but NOT differentiable (SELECT ALL THAT APPLY)

• -5

• -2

• 0

• 1

• 3

x values where the function is not continuous. SELECT ALL THAT APPLY

• -4

• 0

• 5

• 6

Tags

CCSS.HSF-IF.C.7D

x values where the function is continuous but NOT differentiable. Select all that apply

• -4

• 0

• 5

• 6