Subjects calculus

Table Variation Dcad28

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1. The problem asks to find the table of variation of the function $g(x)$ based on the images provided. 2. Since the images are not accessible, I will explain how to find a table of variation for a general function $g(x)$. 3. The table of variation shows intervals where the function is increasing or decreasing and the values of $g(x)$ at critical points. 4. To find it, first compute the derivative $g'(x)$. 5. Solve $g'(x) = 0$ to find critical points. 6. Determine the sign of $g'(x)$ on intervals between critical points. 7. If $g'(x) > 0$ on an interval, $g(x)$ is increasing there; if $g'(x) < 0$, $g(x)$ is decreasing. 8. Evaluate $g(x)$ at critical points to find local maxima or minima. 9. Summarize this information in a table showing intervals, sign of $g'(x)$, and behavior of $g(x)$. Without the explicit function $g(x)$, this is the general method to find its table of variation.