Differentiability

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

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.

Select all the functions that are continuous and differentiable for all real numbers.

• Polynomial Function

• Logarithmic Function

• Absolute Value Function

• Cosine Function

• Cube Root Function

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

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

• TRUE

• FALSE

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.

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?

• 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.