Quiz #1: Differentiability and Derivatives

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.

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

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.

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.HSA.CED.A.2

Graph of a function is given. Where is the function continuous yet NOT differentiable?

• x = a, b, c, d

• x = b, c, d

• x = a, b,

• x = b, d

Where is the function shown in the graph not differentiable?

• x = -2, -1, 0, 1

• x = -2, -1, 1

• x = -2, -1

• x = -1,

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x²