Question

the function g(x) Is the graph below resulted from shifting the graph of f(x) down 2 units. If f’(2)=8, what is g’(2)?

Answer 1

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:

$g(x)=f(x)-2$

Taking the derivative:

$g^{\prime}(x)=f^{\prime}(x)$

This is because the derivative of a constant number is 0. Finally, evaluating at x = 2:

$\begin{gathered} g^{\prime}(2)=f^{\prime}(2) \\ \\ \therefore g^{\prime}(2)=8 \end{gathered}$