Left-and Right-Hand Derivatives...2

[nycmathguy]

Calculus
Section 2.8

Please, work out 65 in step by step fashion.
Also, I would like for you to create YOUR OWN questions 64 and 65 involving "easy" functions (functions other than piecewise functions) for me to do this weekend. We end Section 2.8 and Chapter 2 here.

 

[MathLover1]

a.
look at derivative of each piece

(d/dx)(0) =0 , x<=0
(d/dx)(5-x)=-1 , 0<x<4.........................as a->4 from the left => f -'(a)=-1
(d/dx)(1/(5-x)) = 1/(5 - x)^2 , x>=4.........as a->4 from the right => f +'(a)=1

b.

c. discontinuous at x=0 and x=4
d. at x=4 is not differentiable

 

[nycmathguy]

a.
look at derivative of each piece

(d/dx)(0) =0 , x<=0
(d/dx)(5-x)=-1 , 0<x<4.........................as a->4 from the left => f -'(a)=-1
(d/dx)(1/(5-x)) = 1/(5 - x)^2 , x>=4.........as a->4 from the right => f +'(a)=1

b.
View attachment 3474

c. discontinuous at x=0 and x=4
d. at x=4 is not differentiable

I will need to read this over a few more times.

 

[MathLover1]

pay attention to 3rd example, similar to 65

 

[nycmathguy]

pay attention to 3rd example, similar to 65

Ok. I will watch the clip.

 

[nycmathguy]

pay attention to 3rd example, similar to 65

Terrible video.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Really? All correct? Wow! I did it without the horrible video clip.