# Left-and Right-Hand Derivatives...2

Discussion in 'Calculus' started by nycmathguy, Jun 11, 2022.

1. ### nycmathguy

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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.

nycmathguy, Jun 11, 2022

2. ### MathLover1

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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

MathLover1, Jun 11, 2022
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3. ### nycmathguy

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

nycmathguy, Jun 11, 2022
4. ### MathLover1

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pay attention to 3rd example, similar to 65

MathLover1, Jun 11, 2022
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5. ### nycmathguy

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Ok. I will watch the clip.

nycmathguy, Jun 11, 2022
6. ### nycmathguy

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Terrible video.

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nycmathguy, Jun 11, 2022
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7. ### MathLover1

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correct

MathLover1, Jun 11, 2022
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