Anti Turunan

\begin{equation*}
\begin{split}
f''(x) & = 6x + 1 \\\\
f'(x) & = \int 6x + 1 \: dx \\\\
f'(x) & = 3x^2 + x + c
\end{split}
\end{equation*}

Substitusi \(f'(-1) = 2\)

\begin{equation*}
\begin{split}
f'(x) & = 3x^2 + x + c \\\\
2 & = 3(-1)^2 - 1 + c \\\\
c & = 0
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
f'(x) & = 3x^2 + x \\\\
f(x) & = \int 3x^2 + x \: dx \\\\
f(x) & = x^3 + \tfrac 12 x^2 + d
\end{split}
\end{equation*}

Substitusi \(f(1) = 4,5\)

\begin{equation*}
\begin{split}
f(x) & = x^3 + \tfrac 12 x^2 + d \\\\
4,5 & = 1^3 + \tfrac 12 \:.\: 1^2 + d \\\\
d & = 3
\end{split}
\end{equation*}

\begin{equation*}
\begin{split}
f(x) & = x^3 + \tfrac 12 x^2 + 3 \\\\
f(2) & = 2^3 + \tfrac 12 \:.\: 2^2 + 3 \\\\
f(2) & = 13
\end{split}
\end{equation*}