Seatwork: Differentiability Implies Continuity

If a function is differentiable at a point, then it is continuous at the same point.

• Sometimes True

• Always True

• Never True

If a function is continuous at a point, then it is differentiable at the same point.

• Sometimes True

• Always True

• Never True

If a function is differentiable at a point, then it is not continuous at the same point.

• Sometimes True

• Always True

• Never True

If a function is not differentiable at a point, then it is continuous at the same point.

• Sometimes True

• Always True

• Never True

If a function is not continuous at a point, then it is not differentiable at the same point.

• Sometimes True

• Always True

• Never True

Determine whether the function is differentiable at x = - 4.

• Differentiable

• Not Differentiable

Determine whether the function is differentiable at x = - 3.

• Differentiable

• Not Differentiable

Determine whether the function is differentiable at x = 0.

• Differentiable

• Not Differentiable

Determine whether the function is differentiable at x = -2.

• Differentiable

• Not Differentiable

Determine whether the function is differentiable at x = 2.

• Differentiable

• Not Differentiable