1. The problem states that the function $f$ is differentiable and increasing on the interval $0 \leq x \leq 6$, and that $f$ has exactly two points of inflection on this interval. 2. Since $f$ is increasing, its derivative $f'$ must be non-negative on the interval $0 \leq x \leq 6$. 3. Points of inflection of $f$ correspond to points where the concavity changes, which means the second derivative $f''$ changes sign. 4. Since $f'$ is the first derivative, the points of inflection of $f$ correspond to points where $f'$ has local maxima or minima (extrema), because $f'' = (f')'$. 5. The problem states there are exactly two points of inflection, so $f'$ must have exactly two extrema on the interval. 6. Now, analyze the graphs: - Graph A shows a curve that increases, flattens, then increases sharply again, which suggests two extrema (a maximum and a minimum). - Graph B shows a curve that rises to a maximum then decreases, so only one extremum. - Graph C shows a curve that rises, dips down (a minimum), then rises sharply again, which also suggests two extrema. 7. Since $f$ is increasing, $f'$ must be non-negative. Graph C dips below zero (negative values), so it cannot represent $f'$. 8. Graph A remains non-negative and has two extrema, matching the conditions. Final answer: The graph of $f'$ could be Graph A.