3.4 Lösning 3c

\( {\color{White} x} \qquad \underline{x_1 = 2} \, \):

\[ f''(x) \, = \, 8\,x \]

\[ f''(2) \, = \, 8\cdot 2 = 16 > 0 \quad \Longrightarrow \quad x_1 = 2 \quad {\rm lokalt\;minimum.} \]

\( {\color{White} x} \qquad \underline{x_2 = -2} \, \):

\[ f''(-2) \, = \, 8\cdot (-2) = -16 < 0 \quad \Longrightarrow \quad x_2 = 5 \quad {\rm lokalt\;maximum.} \]

\[ f''(2) \neq 0 \quad {\rm och} \quad f''(-2) \neq 0 \quad \Longrightarrow \quad f(x) \, {\rm har\;inga\;terasspunkter.} \]