A function is increasing and concave up on the interval
MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change
Problem
A function f is increasing and concave up on the interval [2,8]. Four equal-width subintervals are used to create three different Riemann sums:
• one that samples at the left endpoints,
• one that samples at the right endpoints, and
• one that samples at the halfway point of each subinterval.
Which ordering of the three sums must be true?
(a) Left-endpoint sum < Right-endpoint sum < Halfway-point sum
(b) Right-endpoint sum < Left-endpoint sum < Halfway-point sum
(c) Left-endpoint sum < Halfway-point sum < Right-endpoint sum
(d) Halfway-point sum < Left-endpoint sum < Right-endpoint sum