Suppose f is twice differentiable and concave up on [a,b]. Let Tn be the approximation of the average value of f on [a,b] obtained by first estimating ∫abf(x)dx with the Trapezoidal Rule using n equal subintervals and then dividing by b−a. Which of the following best describes the sign of Tn minus the exact average value?
a) Negative, because the trapezoids lie below the curve on a concave-up interval.
b) Positive, because the trapezoids lie below the curve on a concave-up interval.
c) Positive, because the trapezoids lie above the curve on a concave-up interval.
d) Zero, because the trapezoidal estimate is exact for concave-up functions.