Mathematics

When a function is concave up (positive second derivative), its graph curves above its tangent line. Since the linear approximation $L(x)$ is built from the tangent line at $x=2$, and $h$ bends upward away from this line, the actual function value $h(2.4)$ must lie above the approximation. This is the key insight: concavity determines whether the function overshoots or undershoots its linear approximation.

When a function is concave up (positive second derivative), its graph curves above its tangent line. Since the linear approximation $L(x)$ is built from the tangent line at $x=2$, and $h$ bends upward away from this line, the actual function value $h(2.4)$ must lie above the approximation. This is the key insight: concavity determines whether the function overshoots or undershoots its linear approximation.