Let be twice differentiable on with and for all in this interval

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

q

be twice differentiable on

[0,2]

with

q'(x)>0

and

q''(x)<0

for all

x

in this interval. Using equal subintervals of width

\Delta x=0.5

, a student computes a left Riemann sum

L

and a trapezoidal sum

T

to approximate

\displaystyle \int_0^2 q(x)\,dx = I

. Which of the following inequalities must be true? (a)

T < L < I

(b)

L < I < T

(c)

L < T < I

(d)

I < L < T