TeX Quellcode:

\begin{array}{rclll} \mathbb{D} &=& \left]\dfrac{8-\sqrt{70}}{6};\dfrac{8+\sqrt{70}}{6}\right[ \cr\cr f(x) &=& \left(-6x^2+16x+1\right)^{\frac{1}{2}} \cr\cr\cr f'(x) &=& \frac{1}{2}\left(-6x^2+16x+1\right)^{-\frac{1}{2}}\cdot (-12x+16) \cr\cr &=& \dfrac{-6x+8}{\sqrt{-6x^2+16x+1}} \cr\cr &=& (-6x+8)\left(-6x^2+16x+1\right)^{-\frac{1}{2}} \cr\cr\cr f''(x) &=& -6\cdot\left(-6x^2+16x+1\right)^{-\frac{1}{2}} + (-6x+8)\cdot\left(-\frac{1}{2}\right)\left(-6x^2+16x+1\right)^{-\frac{3}{2}}\cdot (-12x+16) \cr\cr &=& \dfrac{-6}{\left(-6x^2+16x+1\right)^{\frac{1}{2}}} + \dfrac{(-6x+8)\left(-\frac{1}{2}\right)(-12x+16)}{\left(-6x^2+16x+1\right)^{\frac{3}{2}}} \cr\cr &=& \dfrac{-6\left(-6x^2+16x+1\right)}{\left(-6x^2+16x+1\right)^{\frac{1}{2}}\left(-6x^2+16x+1\right)} + \dfrac{(-6x+8)\left(-\frac{1}{2}\right)(-12x+16)}{\left(-6x^2+16x+1\right)^{\frac{3}{2}}} \cr\cr &=& \dfrac{-70}{\left(-6x^2+16x+1\right)^{\frac{3}{2}}} \end{array}