1. The problem asks to find the derivative of the function $f(x)$ at the point where $x=1$, denoted as $f'(1)$. 2. The derivative at a point is the slope of the tangent line to the graph of the function at that point. 3. From the graph, the tangent line at $(1,3)$ is shown as a dashed line. 4. To find $f'(1)$, we need to calculate the slope of this tangent line. 5. The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 6. From the graph, the tangent line passes through $(1,3)$ and approximately $(3,1)$ (reading from the graph where the dashed line crosses grid points). 7. Calculate the slope: $$m = \frac{1 - 3}{3 - 1} = \frac{-2}{2} = -1$$ 8. Therefore, the derivative of $f$ at $x=1$ is: $$f'(1) = -1$$ This means the function is decreasing at $x=1$ with a slope of $-1$.