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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)?

the function g(x) Is the graph below resulted from shifting the graph of f(x) down-example-1
User VdesmedT
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1 Answer

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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}

User Vinayak Dornala
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