$f(x_0)f(x\_0)$ berechnen

$f(2)=-{\displaystyle \frac{1}{2}}\cdot 2^4+3\cdot 2=-2f(2)=-\backslash dfrac\{1\}\{2\}\backslash cdot\; 2^4+3\backslash cdot\; 2=-2$

$f^{\mathrm{\prime }}(x)f\text{'}(x)$ bestimmen

$f^{\mathrm{\prime }}(x)=-2x^3+3f\text{'}(x)=-2x^3+3$

$f^{\mathrm{\prime }}(x_0)f\text{'}(x\_0)$ berechnen

$f^{\mathrm{\prime }}(2)=-2\cdot 2^3+3=-13f\text{'}(2)=-2\backslash cdot\; 2^3+3=-13$

$f(x_0),f^{\mathrm{\prime }}(x_0),x_{0}f(x\_0),f\text{'}(x\_0),x\_0$ in Formel einsetzen

$f_t(x)=-13(x-2)+(-2)f\_t(x)=-13(x-2)+(-2)$

$f(x_0)f(x\_0)$ berechnen

$f(3)=-{\displaystyle \frac{1}{2}}\cdot 1^4+3\cdot 1=2,5f(3)=-\backslash dfrac\{1\}\{2\}\backslash cdot\; 1^4+3\backslash cdot\; 1=2\{,\}5$

$f^{\mathrm{\prime }}(x)f\text{'}(x)$ bestimmen

$f^{\mathrm{\prime }}(x)=-2x^3+3f\text{'}(x)=-2x^3+3$

$f^{\mathrm{\prime }}(x_0)f\text{'}(x\_0)$ berechnen

$f^{\mathrm{\prime }}(1)=-2\cdot 1^3+3=1f\text{'}(1)=-2\backslash cdot\; 1^3+3=1$

$f(x_0),f^{\mathrm{\prime }}(x_0),x_{0}f(x\_0),f\text{'}(x\_0),x\_0$ in Formel einsetzen

$f_n(x)=-1(x-1)+2,5f\_n(x)=-1(x-1)+2\{,\}5$