Question

A trapezoidal sum is an underestimate when the function is.

Answer 1

Answer: Concave down

Explanation:

An example is shown below. We have the concave down parabola $y = -x^2+7$ marked in red. The trapezoidal sum is in blue. The three trapezoids combine to something just a bit smaller than the true area under the curve from x = -2 to x = 1. Therefore, this trapezoidal sum is an underestimate of the true area under the curve.

Every part of each trapezoid is completely below the red curve. In other words, no part of the blue pieces spill above the parabola.