V.

H.

Eje x

Eje y

Asíntotas

O.

Cortes con ejes

Derivada primera

Recta tangente

Derivada segunda

Extremos relativos

Puntos de inflexión

Pendiente

Punto sobre f(x)

+

+

+

+

+

+

−

−

−

-

−

−

1

f(x)

2

3

4

1

2

3

4

f(x)=\sqrt{ax^2+bx+c}

f(x)=\frac{\sqrt{bx+c}}{b'x+c'}

f(x)=\frac{bx+c}{\sqrt{b'x+c'}}

f(x)=\sqrt{\frac{bx+c}{b'x+c'}}

f'(x)

tipo: 1
c = -2 (slider from -6 to 6, step 1)
b = 3 (slider from -6 to 6, step 1)
a = 2 (slider from -6 to 6, step 1)
p_1(x) = (a * x^(2)) + (b * x) + c
p = Simplify(p_1)
a' = 0 (slider from -6 to 6, step 1)
b' = 1 (slider from -6 to 6, step 1)
c' = 0 (slider from -6 to 6, step 1)
q_1(x) = (a' * x^(2)) + (b' * x) + c'
q = Simplify(q_1)
asv: false
ash: false
corx: false
cory: false
as = false
aso: false
cor = false
i = false
j = false
k = false
h = false
o: false
u = false
escala = 1 (slider from 0.5 to 10, step 0.5)
v = false
w = false
a_1: false
b_1 = false
f = If(tipo ≟ 1, sqrt(p(x)), tipo ≟ 2, sqrt(p(x)) / q(x), tipo ≟ 3, p(x) / sqrt(q(x)), tipo ≟ 4, sqrt(p(x) / q(x)))
lista3 = Asymptote(f)
P = Point(f)
t = Tangent(P, f)
m = Slope(t)
texto1: "f(x)=" + (LaTeX[f]) + ""
M_2 = NaN
lista6: {}
D = Intersect(f, yAxis, (0, 1.4142135623730951))
texto3: "f(x)=" + (LaTeX[f]) + ""
f'(x) = f'(x)
A = Intersect(f, xAxis, (-0.6666666666666666, 0))
C' = Intersect(f, yAxis, (0, 1.4142135623730951))
r: p
B, E = Intersect(r, xAxis)
I = Extremum(f, -20, 20)
F = Intersect(q, xAxis)
d = OrthogonalLine(F, xAxis)
ashor = Limit(f, Infinity)
e: y = ashor
m1 = Limit(f(x) / x, Infinity)
n1 = Limit(f(x) - (m1 * x), Infinity)
m2 = Limit(f(x) / x, -Infinity)
n2 = Limit(f(x) - (m2 * x), -Infinity)
g = Element(lista3, 1)
g' = Element(lista3, 2)
texto7: "f'(x)=" + (LaTeX[f']) + ""
texto8 = LaTeX(lista3, true, true)