Let \( f(x)=(x-3)^{-2} \). Find all values of \( c \) in \( (1,7) \) such that \( f(7)-f(1)=f^{\prime}(c)(7-1) \). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) \[ c=\square \]
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Step 1: Given the function \( f(x) = (x-3)^{-2} \), we need to find the values of \( c \) in the interval \( (1,7) \) such that \( f(7) - f(1) = f'(c)(7-1) \). Show more…
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