Continuity and Differentiability

One of the conditions a function must satisfy to be continuous at x=c is "f(c) must exist"

• TRUE

• FALSE

Tags

CCSS.HSF.BF.B.3

Which of the following best describes the continuity at x = 1?

• Continuous

• Removable Discontinuity

• Infinite Discontinuity

• Jump Discontinuity

Tags

CCSS.HSF-IF.C.7B

Is the above function differentiable at

x = 0? Why?

• Yes. The derivative would be equal to zero since there is a vertical tangent.

• No. The derivative would not exist at x = 0 since there is a vertical tangent.

• No. The derivative does not exist since the function is not continuous.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Is the above function differentiable for all values of x? Why?

• Yes, the slope of the tangent line can be calculated for all values of x.

• Yes, the function is continuous for all values of x so the function is differentiable.

• No, the function has a sharp turn in the first quadrant so if is not differentiable.

• No, the function is discontinuous so it is not differentiable.

Tags

CCSS.HSA.REI.D.10

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

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

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

• x = -1

• x = 0

• x = 2

• x = 3; x = -2

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Is the function continuous, differentiable, both, or neither?

• continuous

• differentiable

• both

• neither

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

If a function is differentiable, it is also continuous.

• Yes

• No

• It all depends on the function in question.

• TRUE

• FALSE