Differentiability & Continuity

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 = 8

• is differentiable at x = 8

• has a limit that exists at x = 8

• exists at x = 8

Tags

CCSS.HSF.IF.A.2

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

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

A function is continuous at a number c if and only if 

 $f\left(c\right)=\lim_{x\rightarrow c}f\left(x\right)$  

• TRUE

• FALSE

Which is not continuous at x=4?

•  $f\cdot g$  

•  $\frac{f}{g}$  

•  $\frac{g}{f}$  

•  $g^2$  

Tags

CCSS.HSF-BF.A.1B

For what x value, if any, is the function below neither continuous nor differentiable?

 $f\left(x\right)=\frac{2-x}{\left|2-x\right|}$  

(a)