f(x)

V.

H.

Numerador

Denominador

Eje x

Eje y

Asíntotas

O.

Cortes con ejes

Derivada primera

m

Recta tangente

Derivada segunda

Extremos relativos

Puntos de inflexión

Pendiente

Punto sobre f(x)

2

3

4

5

6

7

8

+

+

+

+

+

+

−

−

−

−

−

−

f'(x)

f''(x)

1

c' = -1 (slider from -6 to 6, step 1)
b' = 0 (slider from -6 to 6, step 1)
a' = 1 (slider from -6 to 6, step 1)
d(x) = (a' * x^(2)) + (b' * x) + c'
q = Simplify(d)
a = 1 (slider from -6 to 6, step 1)
b = -1 (slider from -6 to 6, step 1)
c = 2 (slider from -6 to 6, step 1)
f_1(x) = ((a * x^(2)) + (b * x) + c) / ((a' * x^(2)) + (b' * x) + c')
f = Simplify(f_1)
asv: false
lista1: {}
n(x) = (a * x^(2)) + (b * x) + c
ash: false
texto1: "f(x)=" + (LaTeX[f_1]) + "=" + (LaTeX[f]) + ""
corx: false
cory: false
as = false
aso: false
cor = false
r = Div(n, d)
s = Degree(d)
i = false
j = false
k = false
h = false
gd = Degree(q)
p = Simplify(n)
gn = Degree(p)
P = Point(f_1)
t = Tangent(P, f_1)
m_1 = Slope(t)
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
texto4: "f(x)=" + (LaTeX[f]) + ""
lista2 = Asymptote(f)
C = Intersect(f_1, yAxis, (0, -2))
f'(x) = f'(x)
D = Intersect(f', xAxis, (0.17157287515164407, 6.135266792816012E-10))
e = OrthogonalLine(D, xAxis)
G' = Intersect(f', xAxis, (0.17157287515164407, 6.135266792816012E-10))
c_1 = OrthogonalLine(G', xAxis)
A, B = Intersect(p, xAxis)
H' = Intersect(f', xAxis, (0.17157287515164407, 6.135266792816012E-10))
d_1 = OrthogonalLine(H', xAxis)
H = Intersect(f_1, d_1, (0.17157287515164407, -1.914213562373095))
texto5: "f'(x)=" + (LaTeX[f']) + ""
f''(x) = f''(x)
I' = Intersect(f'', xAxis, (-37.37228475164503, 0))
e_1 = OrthogonalLine(I', xAxis)
J' = Intersect(f', xAxis, (0.17157287515164407, 6.135266792816012E-10))
g_1 = OrthogonalLine(J', xAxis)
L = Intersect(f'', xAxis, (-37.37228475164503, 0))
M = Intersect(f'', xAxis, (-37.37228475164503, 0))
h_1 = OrthogonalLine(L, xAxis)
i_1 = OrthogonalLine(M, xAxis)
der1(x) = ((((2 * a) * x) + b) * q(x)) - ((((2 * a') * x) + b') * p(x))
m = Simplify(der1)
E1, E2 = Root(m)
j_1 = OrthogonalLine(E2, xAxis)
k_1 = OrthogonalLine(E1, xAxis)
E' = Intersect(f_1, j_1, (5.82842712474619, 0.914213562373095))
E = Intersect(f_1, k_1, (0.1715728752538099, -1.914213562373095))
g(x) = (m'(x) * q(x)^(2)) - ((2 * q(x)) * m(x))
p_1(x) = (m'(x) * q(x)) - ((2 * m(x)) * q'(x))
q_1 = Simplify(p_1)
F, G, I_1 = Root(q_1)
l = OrthogonalLine(G, xAxis)
l_1 = OrthogonalLine(I_1, xAxis)
J = Intersect(f_1, l, (0.5773502691896257, 0.25000000000000006))
I = Intersect(f_1, l_1, (0.5320888862379565, 0.1559703712540148))
K1, N, O = Intersect(q_1, xAxis)
n_1 = OrthogonalLine(F, xAxis)
K = Intersect(f_1, n_1, (8.694644203726146, 0.9236610509315364))
texto6: "f''(x)=" + (LaTeX[f'']) + ""
texto7: "m=" + (LaTeX[m_1]) + ""