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Matemática
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En este documento encontrarás específicamente contenido de la asignatura de matemática. Solamente teoría de los siguientes temas: Parábola, cónicas, integrales, aplicación de derivadas
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APUCACION DEPUNIOS DE INF(EXION Cambio)
Aplicaion de caleulo difeetncial en laj qut ma funt1on cambia de ser
Crcci ente a de crecientt o vl ceversa.
Para hallarlo k caltuia la primera deriyaaa (x) y posieriormen
te se eemplaa en ia funcion original (y)
Punto máximo
Si ma fumcion continua es as cendente en vn intQrvalo y padir
ae m puniocualguie ra empieza a deerecer
Conoce Comopunto maxino
4
Puntominimo
Si ma función Contin ua es decrecieNte en cierto intervalo hasta vm
punio en l cUal empìca a ascender d este punto Lo Lamanmo3
pimto mini mo.
Para colcular n punto máximo o minimo Se debe calcular la
segmda
deriyada de la funcion origi naly re emplaza loJ valores de (a vaiable
ey se clettrminará si esmaximo o mini moa parti del siqno
del
valor obténidol:
Positivo Cs vm punto minimo
Negati vO un punto máximo.
, IntegraleK
inttgrales o Inttgiates Inteqrates
Antiderivadag definidas indefinidas
Una funcion F Ise denomina (onjunto de todos las antideri
antidevado b inttgrat de va as de la fun.cion flx), se
la fumcion f en mintrvlo
I S f'(K) f(x) paialtodo
valor de x en elintealo SiF) 5 articderivaad de loa
fG) entonees
S foo dx EEbt C, Nint f(k) dz =Fx)HC
Gjemplos:
Sfmboio =
F'X)= 2x X I
b Cada elemento debe sRr escnto
6O) = 4x³tx (7 hasta que Itsuelva ia intqral.
6'X) = 42t2x
HX)= 4x? +x
inteqral de fox) rtspecto a X es
igual a F(X) más c"
INTEGRALES INHEDIATAS f(x): funcion a intgrar
dx dferencat (indica vauiable).
c = constante
2 dx Ejemplos &
2dX
3)
2dx 2(Xtc)
4 2 dx 2x + 2c dos weces Una constant
es l mimo N
nt1
2X t C
Lo )tC
Comprobación
(2x+ )
2
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