We know that the graph of g(x) is the result of a shift of 2 units down from f(x).
Then, f(x) and g(x) are related by:
[tex]g(x)=f(x)-2[/tex]
Taking the derivative:
[tex]g^{\prime}(x)=f^{\prime}(x)[/tex]
This is because the derivative of a constant number is 0. Finally, evaluating at x = 2:
[tex]\begin{gathered} g^{\prime}(2)=f^{\prime}(2) \\ \\ \therefore g^{\prime}(2)=8 \end{gathered}[/tex]
