The function x2−3x+6 is concave.

Question

The function x2−3x+6 is concave.

BlackTom AI · Accepted Answer

Consider the function f(x) = x^2 - 3x + 6. To determine concavity, we examine the second derivative. 
f'(x) = 2x - 3, so f''(x) = 2, which is a positive constant. A positive second derivative indicates the graph is convex (concave up) everywhere on its domain, not concave. Therefore, the statement about concavity as written describes a property opposite to what the function actually has. If a function is concave, we would expect f''(x) ≤ 0 for all x, which is not the case here. The positive curvature means the parabola opens upward, with a U-shape, and it is not concave downward anywhere on its domain. In summary, a constant positive second derivative confirms convexity rather than concavity for this quadratic.

ECON5005 (ND) Quiz 2 -2025 S1

The function x2−3x+6 is concave.

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