Differentiability Intro

Choose all that Apply. A function is "not differentiable" at a point 'x=a',

if :

• The function is not continuous at x = a

• There is a vertical tangent at x = a

• The left hand derivative does not equal the right hand derivative

• There is a horizontal tangent at x = a.

At 'A', choose all true statements.

• The function is continuous

• The function has a vertical tangent line

• The function is "differentiable"

• f ' (A) exists

At 'B', choose all true statements.

• The function is continuous

• The "left hand derivative" does not equal the "right hand derivative"

• The function is "differentiable"

• f ' (B) exists

• $\lim_{h\rightarrow0}\ \frac{f\left(B-h\right)-f\left(B\right)}{h}\ne\lim_{h\rightarrow0}\ \frac{f\left(B+h\right)-f\left(B\right)}{h}$

At 'C', choose all true statements.

• The function is continuous

• The function is "differentiable"
  

• f ' (C) exists
  

• None of the statements are true. 

Tags

CCSS.HSF-IF.C.7B

At 'D', choose all true statements.

• The function is continuous

• The function is "differentiable"
  

• f ' (D) exists
  

• None of the statements are true. 

Tags

CCSS.HSF-IF.C.7B

Which of the following is true at x = 5? Select all that apply. Assume h>0 (h positive)

• f(x) is continuous

•  $\lim_{h\rightarrow0}\ \frac{f\left(5-h\right)-f\left(h\right)}{h}=10$  (L.H.D.)

•  $\lim_{h\rightarrow0}\ \frac{f\left(5+h\right)-f\left(5\right)}{h}=10$   (R.H.D.)

• The Left Hand Derivative = The Right Hand Derivative

• The function is differentiable at x = 5

Is f(x) continuous at x = 3?

• Yes

• No

 $\lim_{h\rightarrow0}\ \frac{f\left(3-h\right)-f\left(3\right)}{h}=$  
(h >0 , Left Hand Derivative)

 $\lim_{h\rightarrow0}\ \frac{f\left(3+h\right)-f\left(3\right)}{h}=$  
(h>0  , right hand derivative)

 $\lim_{h\rightarrow0}\ \frac{f\left(3-h\right)-f\left(3\right)}{h}=\lim_{h\rightarrow0}\ \frac{f\left(3+h\right)-f\left(3\right)}{h}$  
Yes or No ?

• Yes

• No