Answer is: option3

Solution:

Trapezoidal Rule Behavior:

1. Trapezoid sums underapproximate when the function is concave down (∩ shape).
2. Trapezoid sums overapproximate when the function is concave up (∪ shape).

Right Riemann Sum Behavior:

1. Right Riemann sums overapproximate when the function is increasing.
2. Right Riemann sums underapproximate when the function is decreasing.

So we need a function that is:

1. Concave down
2. Increasing

1. (A) Decreasing and concave down → Right Riemann sum would underapproximate. ❌
2. (B) Increasing and concave up → Trapezoid would overapproximate. ❌
3. (C) Increasing and concave down → ✔ This matches both clues.
4. (D) Decreasing and concave down → Right Riemann underapproximates. ❌

Option C