f(x)

Grado 1

Grado 2

| f(x) |

f ' (x)

|f(x)|'

Grado 1

Grado 2

Puntos en que |f(x)| no es derivable

f(x)=a x +b

f(x)=ax^2+bx+c

Construir | f'(x) |

Zoom −

Zoom +

Punto sobre |f(x)|

Recta tangente a |f(x)|

+

+

+

+

−

−

−

−

a' = 0.35 (slider from -5 to 5, step 1.07)
a = If(a' < 0, floor(a'), a' > 0, ceil(a'))
d = -2 (slider from -5 to 5, step 1)
b = 0 (slider from -5 to 5, step 1)
c = -2 (slider from -5 to 5, step 1)
gr: 1
f_1 = If(gr ≟ 1, (a * x) + b, gr ≟ 2, (a * x^(2)) + (b * x) + c, gr ≟ 3, (a * x^(3)) + (b * x^(2)) + (c * x) + d)
f = Simplify(f_1)
q(x) = (-f(x))
r = Simplify(q)
f1 = true
g(x) = abs(f(x))
f'(x) = f'(x)
g'(x) = g'(x)
va = false
f1': false
va': false
E1 = Corner(1)
E2 = Corner(2)
E3 = Corner(3)
D = Corner(4)
E4 = Corner(4)
poli1 = Polygon({E1, E2, E3, E4})
E, F, G = Intersect(f, xAxis)
nd: false
A: (x(E1), 0)
B: (x(E2), 0)
j = Segment(A, B)
texto4: "a=" + a + ""
texto5: "b=" + b + ""
texto6: "c=" + c + ""
texto7: "d=" + d + ""
h(x) = If[f(x) < 0, r(x), f(x) ≥ 0, f(x)]
texto8: "f(x)=" + (LaTeX[f]) + ""
e: false
zo = 2 (slider from 1 to 2, step 1)
texto11: "|f(x) \left|  \right=" + (LaTeX[h]) + ""
C = Point(j)
i = OrthogonalLine(C, j)
P = Intersect(g, i, (-2.651383399209485, 2.651383399209485))
k = Segment(C, P)
l = Tangent(P, g)
m = Slope(l)
H: (x(C), m)
n: false
o: false