ol.lst-kix_eol46ft40hzs-8.start{counter-reset:lst-ctn-kix_eol46ft40hzs-8 0}.lst-kix_eol46ft40hzs-8 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-8,lower-roman) ". "}.lst-kix_eol46ft40hzs-5 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-5,lower-roman) ") "}.lst-kix_3f1merjrbz6d-3 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-3}ol.lst-kix_3f1merjrbz6d-5.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-5 0}.lst-kix_eol46ft40hzs-6 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-6,decimal) ". "}.lst-kix_eol46ft40hzs-8 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-8}.lst-kix_eol46ft40hzs-7 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-7,lower-latin) ". "}.lst-kix_eol46ft40hzs-3 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-3}.lst-kix_91e3e5vca5ek-0 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-1 > li:before{content:"- "}.lst-kix_eol46ft40hzs-2 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-2}ol.lst-kix_eol46ft40hzs-5.start{counter-reset:lst-ctn-kix_eol46ft40hzs-5 0}ol.lst-kix_3f1merjrbz6d-8.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-8 0}.lst-kix_3f1merjrbz6d-0 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-0,decimal) ". "}.lst-kix_3f1merjrbz6d-2 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-2}ol.lst-kix_eol46ft40hzs-7.start{counter-reset:lst-ctn-kix_eol46ft40hzs-7 0}ol.lst-kix_3f1merjrbz6d-1.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-1 0}.lst-kix_3f1merjrbz6d-1 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-1,lower-latin) ". "}.lst-kix_3f1merjrbz6d-5 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-5}.lst-kix_3f1merjrbz6d-8 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-8}ol.lst-kix_eol46ft40hzs-4.start{counter-reset:lst-ctn-kix_eol46ft40hzs-4 0}ol.lst-kix_3f1merjrbz6d-4.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-4 0}ol.lst-kix_eol46ft40hzs-1.start{counter-reset:lst-ctn-kix_eol46ft40hzs-1 0}ol.lst-kix_3f1merjrbz6d-7.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-7 0}ol.lst-kix_3f1merjrbz6d-0.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-0 0}ol.lst-kix_eol46ft40hzs-3.start{counter-reset:lst-ctn-kix_eol46ft40hzs-3 0}.lst-kix_eol46ft40hzs-6 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-6}ol.lst-kix_eol46ft40hzs-8{list-style-type:none}.lst-kix_3f1merjrbz6d-0 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-0}.lst-kix_eol46ft40hzs-0 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-0}.lst-kix_3f1merjrbz6d-6 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-6}ol.lst-kix_eol46ft40hzs-6{list-style-type:none}ol.lst-kix_eol46ft40hzs-7{list-style-type:none}ol.lst-kix_eol46ft40hzs-4{list-style-type:none}ol.lst-kix_eol46ft40hzs-5{list-style-type:none}ul.lst-kix_91e3e5vca5ek-8{list-style-type:none}ol.lst-kix_eol46ft40hzs-2{list-style-type:none}ol.lst-kix_eol46ft40hzs-3{list-style-type:none}ol.lst-kix_eol46ft40hzs-0{list-style-type:none}ol.lst-kix_eol46ft40hzs-1{list-style-type:none}ol.lst-kix_3f1merjrbz6d-3.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-3 0}ul.lst-kix_91e3e5vca5ek-4{list-style-type:none}ul.lst-kix_91e3e5vca5ek-5{list-style-type:none}.lst-kix_3f1merjrbz6d-5 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-5,lower-roman) ". "}ul.lst-kix_91e3e5vca5ek-6{list-style-type:none}ul.lst-kix_91e3e5vca5ek-7{list-style-type:none}ol.lst-kix_eol46ft40hzs-0.start{counter-reset:lst-ctn-kix_eol46ft40hzs-0 0}.lst-kix_eol46ft40hzs-5 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-5}.lst-kix_3f1merjrbz6d-3 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-3,decimal) ". "}.lst-kix_3f1merjrbz6d-4 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-4,lower-latin) ". "}.lst-kix_3f1merjrbz6d-2 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-2,lower-roman) ". "}.lst-kix_eol46ft40hzs-7 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-7}ol.lst-kix_3f1merjrbz6d-2{list-style-type:none}.lst-kix_91e3e5vca5ek-8 > li:before{content:"- "}ol.lst-kix_3f1merjrbz6d-1{list-style-type:none}ol.lst-kix_3f1merjrbz6d-4{list-style-type:none}.lst-kix_eol46ft40hzs-4 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-4}ol.lst-kix_3f1merjrbz6d-3{list-style-type:none}.lst-kix_91e3e5vca5ek-7 > li:before{content:"- "}ol.lst-kix_eol46ft40hzs-2.start{counter-reset:lst-ctn-kix_eol46ft40hzs-2 0}ol.lst-kix_3f1merjrbz6d-0{list-style-type:none}ol.lst-kix_3f1merjrbz6d-6.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-6 0}.lst-kix_eol46ft40hzs-1 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-1}ul.lst-kix_91e3e5vca5ek-0{list-style-type:none}ul.lst-kix_91e3e5vca5ek-1{list-style-type:none}ul.lst-kix_91e3e5vca5ek-2{list-style-type:none}ul.lst-kix_91e3e5vca5ek-3{list-style-type:none}ol.lst-kix_3f1merjrbz6d-6{list-style-type:none}.lst-kix_91e3e5vca5ek-2 > li:before{content:"- "}ol.lst-kix_3f1merjrbz6d-5{list-style-type:none}.lst-kix_3f1merjrbz6d-6 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-6,decimal) ". "}ol.lst-kix_3f1merjrbz6d-8{list-style-type:none}ol.lst-kix_3f1merjrbz6d-7{list-style-type:none}.lst-kix_eol46ft40hzs-1 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-1,lower-latin) ") "}.lst-kix_3f1merjrbz6d-7 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-7,lower-latin) ". "}.lst-kix_3f1merjrbz6d-8 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-8,lower-roman) ". "}.lst-kix_eol46ft40hzs-0 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-0,decimal) ") "}.lst-kix_eol46ft40hzs-2 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-2,lower-roman) ") "}.lst-kix_3f1merjrbz6d-4 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-4}.lst-kix_3f1merjrbz6d-1 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-1}.lst-kix_91e3e5vca5ek-3 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-4 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-5 > li:before{content:"- "}.lst-kix_eol46ft40hzs-4 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-4,lower-latin) ") "}ol.lst-kix_eol46ft40hzs-6.start{counter-reset:lst-ctn-kix_eol46ft40hzs-6 0}ol.lst-kix_3f1merjrbz6d-2.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-2 0}.lst-kix_eol46ft40hzs-3 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-3,decimal) ") "}.lst-kix_91e3e5vca5ek-6 > li:before{content:"- "}.lst-kix_3f1merjrbz6d-7 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-7}
Ex. Find tangent line of 
2
- Find derivatives… 3-6a (done in problem before)
- Plug in unknown to find slope… 3-6(2)=-9
- Plug unknown into the original equation…
- Put point-slope in point-slope line version… y-(-6)=-9(x-2) or y=-9x+12
Y-(y value) = slope (x-xvalue)
We also discuss several other topics like What are characteristics of a good theory?
Points DerivativeIf you want to learn more check out What are the four types of mutation?
f(0) ≈ 0 f’(0) ≈ 0
f(1) ≈ 1 f’(1) ≈ 2If you want to learn more check out senor plural
f(2) ≈ 4 f’(2) ≈ 4
f(-1) ≈ 1 f’(-1) ≈ 2
↗We also discuss several other topics like Why is fertility harder to measure mortality?
These values are the approximate slope of Don't forget about the age old question of Why is Africa considered as humanity's evolutionary eden?
The tangent line at that point.
If you want to learn more check out What are lipid bilayers?
Velocity
means the velocity at time x
⤷ A negative velocity indicates a backward direction
Derivative Function
or 
When slope of original is unchanging,
the derivative has horizontal lines on
that interval.
Notations original = f(x) / position
First derivative = 
/ 
/
/ velocity
Second derivative = 
/ acceleration
Third Derivative = 
/ jerk
Differentiability
Differentiable → able to take derivative
Non-differentiable → unable to take derivative
- Non-continuous functions - hole, asymptote, jump
- Vertical tangent line
- Corner (or cvsp)
⛤ If original is dis-continuous, derivative must be discontinuous ⛤
⛤ But original can be continuous while derivative is still discontinuous⛤
differentiable ⇒ continuous
Relationship between 
Original
Derivative
Increasing at a
Above x axis (positive)
Decreasing at a
Below x axis (negative)
Horizontal tangent line
X-intercept (0)
Cusp / discontinuous / vertical line
undefined
Positive slope line crosses x axis
Negative slope line crosses x axis
linear
Horizontal line
