Question 35: Let the function f (x) be determined on \(\mathbb{R}\) and have a graph f'(x) as the figure below. Set \(g(x)=f(x)-x\) . The function reaches its maximum at which point in the interval below?

We have \(g^{\prime}(x)=f^{\prime}(x)-1 ; g^{\prime}(x)=0 \Leftrightarrow f^{\prime}(x)=1 \Leftrightarrow \left[\begin{array}{l}x=1\\x=-1\\x=2\end{array}\right\)

Table of signs of g(x):

From the table of signs, it can be seen that g(x) reaches its maximum at \(x=-1 \in(-2 ; 0)\)

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