De functie f (x) = ax − xa

Dit is de functie:


De grafiek van f (x) voor a = 0.00 (de rode lijn),
a = 0.05 (de lichtgroene lijn), a = 0.10 (de oranje lijn),
a = 0.20 (de paarse lijn), a = 0.30 (de donkerblauwe lijn),
a = 0.40 (de grijze lijn), a = 0.50 (de donkerbruine lijn),
a = 0.60 (de lichtbruine lijn), a = 0.70 (de donkergroene lijn),
a = 0.80 (de gele lijn), a = 0.90 (de lichtblauwe lijn)
en a = 1.00 (de violet lijn)

De grafiek van f (x) voor a = 1.0 (de rode lijn),
a = 1.1 (de lichtgroene lijn), a = 1.2 (de oranje lijn),
a = 1.3 (de paarse lijn), a = 1.4 (de donkerblauwe lijn),
a = 1.5 (de grijze lijn), a = 1.6 (de donkerbruine lijn),
a = 1.7 (de lichtbruine lijn), a = 1.8 (de donkergroene lijn),
a = 1.9 (de gele lijn) en a = 2.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = 2.0 (de rode lijn),
a = 2.1 (de lichtgroene lijn), a = 2.2 (de oranje lijn),
a = 2.3 (de paarse lijn), a = 2.4 (de donkerblauwe lijn),
a = 2.5 (de grijze lijn), a = 2.6 (de donkerbruine lijn),
a = 2.7 (de lichtbruine lijn), a = 2.8 (de donkergroene lijn),
a = 2.9 (de gele lijn) en a = 3.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = 3.0 (de rode lijn),
a = 3.1 (de lichtgroene lijn), a = 3.2 (de oranje lijn),
a = 3.3 (de paarse lijn), a = 3.4 (de donkerblauwe lijn),
a = 3.5 (de grijze lijn), a = 3.6 (de donkerbruine lijn),
a = 3.7 (de lichtbruine lijn), a = 3.8 (de donkergroene lijn),
a = 3.9 (de gele lijn) en a = 4.0 (de lichtblauwe lijn)

De grafiek van f (x) voor a = e − 0.5 (de rode lijn),
a = e − 0.4 (de lichtgroene lijn), a = e − 0.3 (de oranje lijn),
a = e − 0.2 (de paarse lijn), a = e − 0.1 (de donkerblauwe lijn),
a = e (de grijze lijn), a = e + 0.1 (de donkerbruine lijn),
a = e + 0.2 (de lichtbruine lijn), a = e + 0.3 (de donkergroene lijn),
a = e + 0.4 (de gele lijn) en a = e + 0.5 (de lichtblauwe lijn)

De grafiek van de nulpunten van f (x):
n1 (de rode lijn) en n2 (de groene lijn)
De tabel hieronder geeft de nulpunten van de functie voor a = 0 tot en met a = 10 in stappen van 0.001 met twintig cijfers achter de komma.
an1n2
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