1. Statement of the problem: We are given the graph of a differentiable function f and the line tangent to the graph at x = 2; find $f'(2)$. 2. Formula and rules: The derivative at a point equals the slope of the tangent line at that point. Use the slope formula $$m=\frac{y_2-y_1}{x_2-x_1}$$. Important rule: To find the slope from two points, take the change in y over the change in x and simplify. 3. Identify points: From the graph the tangent line passes approximately through the points $ (0,2) $ and $ (5,4) $. 4. Compute the slope: Plugging the coordinates into the formula gives $$m=\frac{4-2}{5-0}=\frac{2}{5}$$. 5. Simplify and interpret: Simplifying yields $f'(2)=\frac{2}{5}=0.4$. 6. Final answer: $f'(2)=\frac{2}{5}$.