f'

f'

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f

\text{f'(x) > 0 für\
-\infty < x < -2}

\text{f'(x) < 0 für\-2 < x < 0}

\text{f'(x) < 0 für\0 < x < 2}

\text{f'(x) > 0 für\2 < x < \infty}

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)
Q = Point(f1)
x0: x(Q)
P: (x0, f(x0))
c_{1} = Circle(P, 1)
g = Tangent(P, 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)
hb = Segment(A, B)
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)]
P0: (x0, f(x0))
P1: (x0, f(x0))
P2: (x0, f(x0))
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)