f'

f'

f'

f

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\text{f ist im Intervall -2 < x < 2\
streng monoton fallend}

\text{f ist im Intervall -\infty < x < -2\
streng monoton steigend}

\text{f ist im Intervall 2 < x < \infty\
streng monoton steigend}

f

x_1

x_2

f(x_1)

f(x_2)

c = 0.5 (slider from -1 to 1, step 0.1)
f(x) = (1 / 20 * x^(5)) - (1 / 3 * x^(3)) + c
f1(x) = f'(x)
P1 = Point(f)
x1: x(P1)
Q: (x1, f1(x1))
c_{1} = Circle(P1, 1)
g = Tangent(P1, f)
gl1: x = -2
gl2: x = 0
gl3: x = 2
h0(x) = If[x < -2, f1(x)]
h1(x) = If[-2 < x < 0, f1(x)]
h2(x) = If[0 < x < 2, f1(x)]
h3(x) = If[2 < x, f1(x)]
A, B = Intersect(c_{1}, g)
hr = Segment(A, B)
hs = Segment(A, B)
g0(x) = If[x < -2, f(x)]
g1(x) = If[-2 ≤ x ≤ 2, f(x)]
g2(x) = If[2 < x, f(x)]
N1: (-2, 0)
N2: (0, 0)
N3: (2, 0)
gL = -6 (slider from -10 to 5, step 0.1)
gR = 6 (slider from -5 to 10, step 0.1)
gU = -3 (slider from -5 to 5, step 0.1)
gO = 3 (slider from -5 to 5, step 0.1)
Q0: (x1, f1(x1))
Q1: (x1, f1(x1))
Q2: (x1, f1(x1))
P2 = Point(f)
X1: (x1, 0)
x2: x(P2)
X2: (x2, 0)
s1 = Segment(X1, P1)
s2 = Segment(X2, P2)