f^'(x)=12x^2-6x+1,f(1)=5

Lösung

f^{^{'}} (x) = 12 x^{2} - 6 x + 1, f (1) = 5

f (x) = 4 x^{3} - 3 x^{2} + x + 3

Schritte zur Lösung

f^{'} (x) = 12 x^{2} - 6 x + 1

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

f (x) = \int 12 x^{2} - 6 x + 1 d x

\int 12 x^{2} - 6 x + 1 d x = 4 x^{3} - 3 x^{2} + x + c_{1}

f (x) = 4 x^{3} - 3 x^{2} + x + c_{1}

Wende die Anfangsbedingung an:

f (x) = 4 x^{3} - 3 x^{2} + x + 3

f (x) = 4 x^{3} - 3 x^{2} + x + 3

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