Calculus Integration

Question

Let  be a function whose first derivative  and second derivative  are both positive on the closed interval [a, b]. The interval [a, b] is partitioned into n equal length sub-intervals, and these are used to compute a left-endpoint sum, right-endpoint sum, and trapezoid rule approximations. Which of the following shows the correct ordering?

Your answer:

Answer 1

Since f'(x) > 0, f(x) is increasing on the interval. So, L_n < exact value < R_n. Thus, the second, fourth, and fifth choices can be eliminated.

Since f"(x) > 0, the graph of y = f(x) is concave up. So, the trapezoid rule approximation, T_n, would give an overestimate. So, the first choice gives the correct order.