3.1 Lösning 7c

\[ f(x) = {x^4 \over 4} - 8\,x^2 \]

\[ f\,'(x) = {4\,x^3 \over 4} - 16\,x = x^3 - 16\,x \]

\[\begin{array}{rcl} x^3 - 16\,x & = & 0 \\ x\,(x^2 - 16) & = & 0 \\ x_1 & = & 0 \\ x^2 - 16 & = & 0 \\ x^2 & = & 16 \\ x_2 & = & 4 \\ x_3 & = & -4 \\ \end{array}\]

Derivatan \( \, f\,'(x) = x^3 - 16\,x \, \) har de tre nollställena:

\[\begin{array}{rcl} x_1 & = & 0 \\ x_2 & = & 4 \\ x_3 & = & -4 \\ \end{array}\]