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}`