Which of the following sets of conditions is sufficient to guarantee a number satisfying ?

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Which of the following sets of conditions is sufficient to guarantee a number

c\in(a,b)

satisfying

\displaystyle \int_a^b g(x)\,dx=g(c)(b-a)

? (a)

g

is integrable on

[a,b]

only. (b)

g

is differentiable on

(a,b)

but may be discontinuous at

a

b

. (c)

g

is continuous on

[a,b]

. (d)

g

is bounded on

[a,b]

and has finitely many discontinuities.