$ \frac{dy}{dx} $

Interpolación

Variar perfil

Elegir intervalo

Punto en la gráfica

Punto móvil en eje X

Gráfica

Extremos intervalo

Extremos absolutos

Banda horizontal

% inclinación en P

Tasa de Variación Media

Ángulo de inclinación

Recta de pendiente media

Recta tangente

Vector unitario tangente

Función derivada

Extremos relativos

Vector unitario curvatura

Círculo osculador

Función 2ª derivada

Puntos inflexión

Función área (Animación)

Primitiva de la derivada

a

b

Función

Recorrido o rango

T V M

Primera derivada

Segunda derivada

Integral

0 \; \%

Trapecios

Coordenadas

F(x) =

f0(x) = abs(((x + 1) * sin(x) / 5) + 1.8) + 0.6
f1(x) = 4 - abs(x - 5)
f3(x) = (x - fractionalPart(x)) / 2
f4(x) = If[x < 5, 5 - x^(2) / 10, 12.5 / x - 1]
f5(x) = If[x < 5, 5 - x^(2) / 10, 12.5 / x]
listaF: {"Personalizada", "Valor absoluto", "Cúbica", "Parte entera", "Discontinua", "Punto anguloso"}
elegido = SelectedIndex(listaF)
f2(x) = (x^(3) - (15 * x^(2)) + (63 * x) - 49) / 20
listaFF: {f0, f1, f2, f3, f4, f5}
f = Element(listaFF, elegido)
Vesq1: (0, 1)
Vesq2 = Point(Ray[Vesq1 + (0.2, 0), Vesq1 + (1, 0)])
nada = 0.4 (slider from 0 to 1, step 0.1)
epsilon = 1.0E-6
panel0 = 3 (slider from 1 to 6, step 1)
panel: round(7 - panel0)
J = (-0.75, 2.5)
H = (-0.8866666666666674, 6.14)
I = (1.953333333333338, 2.86)
K = (1.6333333333333375, 1.8)
Se0 = (-4.060000000000001, 3.479999999999998)
Se1: Se0 + (0.88, 1.6)
Se2: Se0 + (1.14, 1.6)
n = 12 (slider from 3 to 20, step 1)
Vesq3 = Point(Ray[Vesq2 + (0, 0.2), Vesq2 + (0, 1)])
ancho: x(Vesq2 - Vesq1)
alto: y(Vesq3 - Vesq1)
m: round(n)
h: ancho / (m - 1)
v = 5 (slider from 1 to 9, step 1)
interpolar = false
elegirPuntos = false
elegirIntervalo = false
verP = true
verX = true
verFuncion = true
verExtremosIntervalo = true
verExtremosAbsolutos = false
verHorizontal = false
verPorcentaje = true
verTVM = true
verAngulo = false
verRectaPendienteMedia = false
verRectaTangente = false
verTangente = true
verDerivada = false
verExtremos = false
verNormal = true
verOsculador = false
verDerivada2 = false
verInflexion = false
verArea = false
verPrimitivaDerivada = false
ff(x) = If[x(Vesq1) ≤ x ≤ x(Vesq2), f]
franjaff: {Polygon[Vesq1 - (0, 20), Vesq2 - (0, 20), Vesq2 + (0, 20), Vesq1 + (0, 20)]}
Aa: (x(Vesq1), ff(Vesq1))
Az: (x(Vesq2), ff(Vesq2))
Extremos: {Extremum[ff, x(Vesq1), x(Vesq2)]}
ExtremosAbs1 = RemoveUndefined(Join[{{Aa}, Extremos, {Az}}])
ExtremosAbs2 = Sort(Sequence[(y(Element[ExtremosAbs1, k]), x(Element[ExtremosAbs1, k])), k, 1, Length[ExtremosAbs1]])
ExtremoAbsMax: (y(Element[ExtremosAbs2, Length[ExtremosAbs2]]), x(Element[ExtremosAbs2, Length[ExtremosAbs2]]))
ExtremoAbsMin: (y(Element[ExtremosAbs2, 1]), x(Element[ExtremosAbs2, 1]))
bandaHorizontalff: {Polygon[{ExtremoAbsMin - (100, 0), ExtremoAbsMin + (100, 0), ExtremoAbsMax + (100, 0), ExtremoAbsMax - (100, 0)}]}
polígono1ff, poli1altura, poli1base, poli1hipotenusa = Polygon(Az, (x(Az), y(Aa)), Aa)
sEff = Segment(((-x(Vesq1)) - 0.6, y(ExtremoAbsMin)), ((-x(Vesq1)) - 0.6, y(ExtremoAbsMax)))
Eff = Point(sEff)
bff: y = y(Eff)
ccff = Circle(Aa, poli1base / 3)
Fff = Intersect(ccff, poli1hipotenusa)
Nff = Intersect(ccff, poli1base)
iff = Ray(Aa, ((x(Az), y(Aa)) + Az) / 2)
Gff = Intersect(ccff, iff)
kff = CircumcircleArc(Fff, Gff, Nff)
αff = Angle(Aa + (1, 0), Aa, Az)
tvmff = Slope(poli1hipotenusa)
F'' = Derivative(f, 2)
ExtremosX = Sequence((x(Element[Extremos, k]), 0), k, 1, Length[Extremos])
extrSegff = Sequence(Segment[Element[Extremos, k], Element[ExtremosX, k]], k, 1, Length[Extremos])
InflexionX: {Roots[F'', x(Aa), x(Az)]}
inflex1: x(InflexionX)
InflexionP = Sequence((Element[inflex1, k], f(Element[inflex1, k])), k, 1, Length[inflex1])
inflexSegP = Sequence(Segment[Element[InflexionP, k], Element[InflexionX, k]], k, 1, Length[InflexionP])
texto3ff: "" + αff + ""
F' = Derivative(f)
textoDf = LaTeX(F', true, true)
textoD2f = LaTeX(F'', true, true)
trapeciosff = TrapezoidalSum(F', x(Vesq1), x(Vesq2), m)
verTrapecios = false
A = (-0.9866666666666676, 0.34)
C = (2, 0.25)
bordePefil: {Polygon[A - (10, 0), (x(A) - 10, y(C)), C + (10, 0), (x(C) + 10, y(A))]}
O = (-1, 1.25)
fondoPanel: {Polygon[H + (-10, 10), (x(H) - 10, y(I)), I + (10, 0), (x(I) + 10, y(H) + 10)]}
bordePefilff: {Polygon[O - (10, 0), (x(O) - 10, y(C)), C + (10, 0), (x(C) + 10, y(O))]}
verCoordenadas = false
bordeInterpolación: {Polygon[J - (10, 0), (x(J) - 10, y(K)), K + (10, 0), (x(K) + 10, y(J))]}
base = Segment((x(Vesq1), 0), (x(Vesq2), 0))
X = Point(base)
P: (x(X), f(X))
segPX = Segment(X, P)
rectaTangente = Line(P, (x(X) + epsilon, f(x(X) + epsilon)))
dgPff = Slope(rectaTangente)
texto1 = RotateText("" + (abs(round((100 * dgPff)))) + " \%", (30° * sgn(dgPff)))
texto1b = RotateText("" + (abs(round((100 * dgPff)))) + " \%", 330°)
dgP: round((dgPff * 1000)) / 1000
tangente = UnitVector(Vector[P, P + (1, dgPff)])
DF: X + (0, dgPff)
lugar1 = Locus(DF, X)
d1 = Segment(P + (1, 0), P + (1, dgPff))
d2 = Segment(X, DF)
rectaPendienteMedia = Line(P, poli1hipotenusa)
d2gP = Iteration(F'', x(X), 1)
normal = Vector(P, Rotate[P + tangente, (sgn(d2gP) * π / 2), P])
radioCurvatura: abs((1 + dgP^(2))^(3 / 2) / d2gP)
circuloOsculador = Circle(P + (radioCurvatura * normal), radioCurvatura)
D2F: (x(X), d2gP)
sXD2F = Segment(X, D2F)
lugar2 = Locus(D2F, X)
D: P - (0, y(Aa))
d2b = Segment(X, DF)
sXDF = Segment(X, DF)
lugar3 = Locus(D, X)
campoDeTexto1 = Textfield(f0)
a: f0((5, 4))
lista1: {(1.90258, 1.94886), (4.88082, 0.24048), (7.96507, 3.18196)}
lista2: {(1.90258, 2.94886), (4.88082, 1.24048), (7.96507, 4.18196)}
dx = 1 (slider from 0.01 to 2, step 0.01)
Xdx: X + (dx, 0)
Xmdx: X - (dx, 0)
Pdx: (x(Xdx), f(Xdx))
Pmdx: (x(Xmdx), f(Xmdx))
sdx = Segment(Pdx, Xdx)
smdx = Segment(Pmdx, Xmdx)
secante = Line(P, Pdx)
secantem = Line(P, Pmdx)