CALC 2.10 Differentiability Classwork

If  $f\left(x\right)$  has a derivative at x = a, then f is continuous at x = a.

• True

• False

Can a function be continuous but not differentiable?

• Yes

• No

True or False: Continuity implies differentiability 

• True
• False

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

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

The graph of a function is given. Which of the following is not true

• Function is continuous at x = 2

• Function is differentiable at x = 2

• Function has a limit that exists at x = 2

• Function exists at x = 2

Where is the function shown in the graph not differentiable?

• x = -2, -1, 0, 1

• x = -2, -1, 1

• x = -2, -1

• x = -1,

The function shown

• is continuous at x = 8

• is differentiable at x = 8

• has a limit that exists at x = 8

• exists at x = 8

Tags

CCSS.HSF.IF.A.2

On what interval(s) is the following function continuous?

• (-∞,-2)u(-2,∞)

• [-2,2]

• (-2,2)

• (-∞,-2]u[-2,∞)

Tags

CCSS.HSF-IF.C.7D

The function, $f\left(x\right)=\frac{x}{x^2-4}$ , is not differentiable at  $x=2$  because the limit of  $f'\left(x\right)$  as x approaches 2 is:  

Answer explanation

 $-\infty$