1. The problem asks: At which point does a tangent line approximation underestimate the function value? 2. Tangent line approximation uses the tangent line at a point to estimate nearby values of the function. 3. Important rule: If the function is concave up (curving upward) at the point of tangency, the tangent line lies below the curve, so the approximation underestimates the function. 4. Conversely, if the function is concave down (curving downward), the tangent line lies above the curve, so the approximation overestimates. 5. From the graph description, the function has local maxima near $x=1$ and $x=7$, indicating concave down near those points. 6. Near $x=0$, the curve is increasing and appears concave up (since it rises from near 0 to a peak at $x=2$). 7. Near $x=6$, the function is near a local maximum, so it is concave down. 8. Near $x=12$, the function is rising again and appears concave up. 9. Therefore, tangent line approximation will underestimate the function near points where the function is concave up, such as near $x=0$ and $x=12$. 10. Among the options, a point of tangency near $x=0$ guarantees an underestimate. Final answer: A point of tangency near $x=0$ guarantees that the tangent line approximation will result in an underestimate.