Summary
Summary Application of Derivatives
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Handwritten cheat sheet for Application of Derivatives by JEE 2020, GATE, and CSIR topper
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Appicaho cf_Dexivahvesskpeflath)-fa)
19
of line jeining ALB
h Ala,Fla
LAs h0,PÅ. tende to
comade coith A by eohich h>
chord AB tends to be a.
tarngent fa)= lim fath)-Fa)
h
=has -ais ag
49gn) oil ave
tangent at orgin
vehcle tangen at xeo
dis entnoug func can aleo hae vertical
tangent
Lhe gzaph af g=fo) has anique non -yertad
tangent at xaa
dferentiable. at na
then he tuncyalFois
H=a B vice --Veksa
LEquation of tangent and Noxmal
The of noneestica tanget atla,fla)
a dy
F'a) danates sope of
angent
"A cuYe =fln) is said tohave a vesthioa
tangent a n=F fa) e fla) both
tesdto0 ox -0 Simultaneousli
The eq.of Yextical tangent at aEa) is
, Noxmal:- Alinel to a tangent to the cume
9fol
42nld e pt of tangenc isS called nçama
he cve. The ean. ef nothal at Ca,Fla)) s
g-fal=
4-fa) = - G-a) JF F'Ca) #o
JE F'Ca)=0
gfoo has a vestioal tangent
O
t he tangent any pt. on he cukve is aqualy
incined to both ais hen dyldu = tL
Tangent to a cLVe at pt can be daun en
hoigh dd does not exist
F hexe atangent to an eren fune. o nso
Tangent Fom an etexnal pt
RCa. b) aohich doesn't he on the cuxve
then the egn
cepaszinghethaoigh la,b) an ho foune
o of contat a
Condition fox ine to be tangeot ox
sope of ine slope af fangent
egth of tangenti- aom ph aE_intoxcechon, ta
intexcept onX-asS
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