21 Derivative of a polynomialfunction
in fans hi rentalfins x
shortcut
power rule
if ya
then y nani
Ex y su Ex y an
one in a
y
35ns
I
iz
ur
Ex yea
y on
i
y o an
o
y a
no
constant rule
if y c car
theny'd
Ex y 3n'tans ans n s
an on to su a
g
tan su r su a
Ex Findtheequation of the tangentline to rim susans n t n
Needslopeand apoint mmbl
ay
mef in
an anti n aslopeof alltangentlines
filmacneact tin a
a
pointin.nl
finean acre in t
o
ii ol
y mntb
y on b
subin ii o
o ontb
b o
i y on o
, Q finssu ansn t ta er
when's the slopeo
Differenciate then y o csettheequation
equal to o solveforn
a fini susansn n
gins an'tn
when'stheirslope of the tangent foreach
the same
fsungin
Fintan
THE CONSTANT MULTIPLERULE
if finian
then fineaf'm aninn
Ex Finian
y 12ns
THEsumANDDIFFERENCERULE
if fourginithen
then fansgiantthin
if Finigininine
thenfilmgin n'in
ExFinisusanti Ex fireman susan
fleurona fanssnotani.sn
Q Determine the equationof thelinetangent to thecurvefinssusans n at net
to findtheequationof alineyoumusthavetheslopeanda point
Recallthatthefirstderivativeto a functionis theequation oftheslopes to thefunction
firm ans anta a
a
fanact acute
fan a at
fine
therefore mo
nowfindthe point of tangencyfall
fill sin ans in i
fan i i
fill c
ptclol
y mntb
youth
sub lol
o ointb
Do
you 6 therefore the equation of the tangentlineis on6
in fans hi rentalfins x
shortcut
power rule
if ya
then y nani
Ex y su Ex y an
one in a
y
35ns
I
iz
ur
Ex yea
y on
i
y o an
o
y a
no
constant rule
if y c car
theny'd
Ex y 3n'tans ans n s
an on to su a
g
tan su r su a
Ex Findtheequation of the tangentline to rim susans n t n
Needslopeand apoint mmbl
ay
mef in
an anti n aslopeof alltangentlines
filmacneact tin a
a
pointin.nl
finean acre in t
o
ii ol
y mntb
y on b
subin ii o
o ontb
b o
i y on o
, Q finssu ansn t ta er
when's the slopeo
Differenciate then y o csettheequation
equal to o solveforn
a fini susansn n
gins an'tn
when'stheirslope of the tangent foreach
the same
fsungin
Fintan
THE CONSTANT MULTIPLERULE
if finian
then fineaf'm aninn
Ex Finian
y 12ns
THEsumANDDIFFERENCERULE
if fourginithen
then fansgiantthin
if Finigininine
thenfilmgin n'in
ExFinisusanti Ex fireman susan
fleurona fanssnotani.sn
Q Determine the equationof thelinetangent to thecurvefinssusans n at net
to findtheequationof alineyoumusthavetheslopeanda point
Recallthatthefirstderivativeto a functionis theequation oftheslopes to thefunction
firm ans anta a
a
fanact acute
fan a at
fine
therefore mo
nowfindthe point of tangencyfall
fill sin ans in i
fan i i
fill c
ptclol
y mntb
youth
sub lol
o ointb
Do
you 6 therefore the equation of the tangentlineis on6
