Differentiability vs Continuity

Can a function be continuous but not differentiable?

• Yes

• No

If a function is differentiable, it is also continuous.

• Yes

• No

• It all depends on the function in question.

The function shown

• is continuous at x = 8

• is differentiable at x = 8

• has a limit that exists at x = 8

• exists at x = 8

Tags

CCSS.HSF-IF.C.7B

The function shown

• is continuous at x = 2

• is differentiable at x = 2

• has a limit that exists at x = 2

• exists at x = 2

Tags

CCSS.HSF-IF.C.7B

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

The function shown

• is continuous at x = 0

• is differentiable at x = 0

• has a limit that exists at x = 0

• exists at x = 0

The function shown

• is continuous at x = b

• is differentiable at x = b

• has a limit that exists at x = b

• exists at x = b

Tags

CCSS.HSF.IF.A.2