Continuity and Differentiability Quiz

What is the relationship between a smooth graph and differentiability?

• A smooth graph is always undefined.

• A smooth graph is never differentiable.

• A smooth graph is always differentiable.

• A smooth graph is always discontinuous.

Which of the following is true about polynomials?

• They are differentiable but not continuous.

• They are neither continuous nor differentiable.

• They are continuous and differentiable everywhere.

• They are continuous but not differentiable.

What happens to differentiability at a vertical tangent line?

• The function is neither continuous nor differentiable.

• The function is continuous but not differentiable.

• The function is only continuous.

• The function is differentiable.

Why is a function not differentiable at a corner?

• Because the slope is always zero.

• Because the graph is not connected.

• Because there is no unique tangent line.

• Because the function is not defined.

What is a cusp in terms of differentiability?

• A point where the function is continuous but not differentiable.

• A point where the function is both continuous and differentiable.

• A point where the function is differentiable but not continuous.

• A point where the function is neither continuous nor differentiable.

What type of discontinuity involves a hole in the graph?

• Jump discontinuity

• Point discontinuity

• Infinite discontinuity

• Vertical discontinuity

Which discontinuity is characterized by a sudden jump in the graph?

• Infinite discontinuity

• Point discontinuity

• Vertical discontinuity

• Jump discontinuity

What is true about differentiability at an endpoint?

• It is not differentiable at the endpoint.

• It is differentiable only if the endpoint is included.

• It is never differentiable.

• It is always differentiable.

In which interval is a semicircle differentiable?

• Nowhere

• Only at its endpoints

• Excluding its endpoints

• Including its endpoints

What is the relationship between continuity and differentiability?

• Neither implies the other.

• Continuity implies differentiability.

• Both imply each other.

• Differentiability implies continuity.