Which of the following statements is sufficient to guarantee that there exists a…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Which of the following statements is sufficient to guarantee that there exists a number

c

[a,b]

for which

f(c)

equals the average value of a real-valued function

f

on that interval? (a)

f

is differentiable on

(a,b)

. (b)

f

is continuous on the closed interval

[a,b]

. (c)

f

is Riemann

\text{–}

integrable on

[a,b]

even if it has jump discontinuities. (d)

f

is continuous only on the open interval

(a,b)